Even with a wetsuit on I was cold. The waters south of Cape Town in SouthAfrica are closer to Antarctica than they are to the tropics. The creature ahead of me was chilling, too: its girth was so huge I couldn't have circled its body with my arms. And its environment was alien to me. In the sea, I was comparatively clumsy, coping with the twin problems of staying afloat and breathing with a snorkel. Unless underwater technology changes radically, we'll always be half blind and deaf in the ocean - but that doesn't mean that what I could see wasn't magnificent. Sunlight splashed onto the shark's eye and the dead black hole transformed itself into a shining blue-black, coming alive in the process. On the side of the creature's head, five gill slats flared open. I imagined I could see the vortices of oxygen-stripped water spiralling away from the clefts, which looked like knife cuts in blotting paper. The five-metre-long animal seemed curious and circled slowly. Its great head was tapered to a point, which is why Australians call the most feared of all sharks the white pointer.

The image of its mouth is forever burned into my consciousness - it was smiling with a clownish grin. This rictus smile was fixed, so the teeth were always on show. The great white shark was thrilling, more like a jet fighter than a fish. If it wanted to it could have given me a devastating, perhaps lethal, bite. I wasn't in a cage and a wetsuit was my only protection (my companion André Hartman had a spear gun, but it didn't work). I didn't want this encounter to end, but after a while the great white became a little too curious and André gave it a sharp rap on the nose with his heavy camera housing and sent it on its way.

This sequence was the finale to a film I produced about the world's largest sharks. My purpose was to show that great whites are not malicious monsters with a taste for human flesh. But then they're not harmless herbivores either - there is no doubt they have the potential to eat us, and that's what makes them so exciting, one of the last predators of humanity.

I would never have dared do what I did if I hadn't spent ten days observing the behaviour of great whites - and nearly the same amount of time reading everything I could about them. I also had a companion who'd swum with great whites hundreds of times before. I'd seen that the great fish are careful about what they bite; white marks, as if a child had scribbled with chalk on their snouts, bore testament to injuries caused by the teeth or claws of fur seals, their main prey. Great whites are cautious before they bite - their eyes are vulnerable. I also knew that they aren't particularly fond of humans as food: we don't have enough blubber to be energy-rich, fur seals are power bars compared to us. Andre had also waited until the visibility was good. In dirty water the sharks couldn't see us clearly and we wouldn't be able to see them.

Most attacks by great whites (there have been 245 since 1846, and of these only 60 were fatal) have been cases of mistaken identity. The hungry shark has seen movement at the surface of the water and has launched a vertical lunge before discovering that it has bitten a human rather than a seal. The predator doesn't even bother delivering the coup de grace to our scrawny bodies, which is why many human victims survive shark attacks.

But even with all this knowledge and my direct experience, I still wouldn't recommend that other travellers swim freely with great whites. By all means, view them from a cage, but even then, without expert help and perfect conditions you could be taking a risk.

Most divers feel elated if they catch a glimpse of a shark. Tales of waters infested with them, just like those of deserts teeming with scorpions or rainforests writhing with venomous snakes, are usually just that, travellers' tales. As a wildlife film-maker, it didn't take me long to find this out. It takes weeks, possibly months, of meticulous planning to ensure that you are in the right place at the right time to get the pictures used in documentaries. If we just turned up on the off chance, with a vague hope of seeing animals, hazardous or otherwise, it's unlikely that any wildlife film would ever be completed. But we do have more opportunities than most other travellers to meet potentially dangerous creatures - and, most importantly, to do so safely.

If you follow a couple of simple rules, shark watching shouldn't be any more hazardous than badger watching. I've dived with tiger sharks, hammerheads and reef sharks without any problems at all. Spear fishing when sharks are around is, of course, a no-no: the blood in the water and the death throes of the punctured fish excite sharks too much so they tend to come too close for comfort. Don't touch or approach sharks too closely, just watch and marvel. If a shark is going to attack, it usually displays warning signs, arching its back, raising its head and lowering its pectoral fins (the big wing- like ones at the front).

If a shark does look likely to attack (this really is a million to one chance), the worst thing you can do is panic and try to flee - the shark is far swifter in the water than you are, and may confuse your flailing behaviour with that of an ailing fish. Instead, stand your ground and remember that the eyes and heads of sharks are vulnerable. If one comes at you, be prepared to give it a punch or even gouge its eyes with your fingernails. If possible, seek a retreat on the reef or rock wall, making sure you keep your back against something solid.

As well as sharks, there are other potentially hazardous animals in the sea. Animals made of jelly, the sea gooseberries, salps, sea butterflies and jellyfish, are some of my favourites - then there's the glories of the plankton, some of which have brightly coloured tentacles or delicate air-filled floats. Others have rows of cilia that flash with iridescent colours when they catch the light. Sea butterflies live up to their name, flapping languidly through the water with transparent wings. Many of these animals, particularly jellyfish, have a battery of stinging cells for catching prey - but they can also lash unwary swimmers.

Most cause nothing worse than a mild prickling or tingling sensation, perhaps with some swelling and reddening of the skin, but stings from the infamous Portuguese man o' war can be excruciating, and those from the box jellyfish lethal. To avoid the former watch out for dead man o' wars washed up on the shore (this creature is usually quite big, with tentacles up to nine metres long that hang from a gas-filled flotation bladder that is tinted with blue, purple and pink). If a few of these are beached, the waters could be infested, so avoid swimming there. If you can't resist a dip, wear long pants and a long-sleeved shirt, as these will give protection from the stinging cells.

The box jellyfish is a different proposition. Travellers need to seek local advice about its presence or watch out for warning signs. It's prevalent in some regions of the Pacific and Indian oceans, particularly in the tropical waters of Australia. This jellyfish has been responsible for the deaths of 90 people to date, and about 70 of these fatalities were in Australian waters. This cube of jelly has four groups of trailing tentacles - blunder into these and they discharge into your skin, causing savage and excruciating pain. There's acute inflammation and a florid flare on the skin where the tentacles have made contact. Venom is absorbed into the bloodstream, attacking the victim's nervous system. I've seen the warning signs about stinger season in northern Australia, and I'd be petrified about swimming at that time without a stinger suit (a thin wetsuit) for protection. If anyone is unlucky enough to get stung, the injured region should be doused with vinegar for a minimum of 30 seconds (there are vinegar supplies on many of the beaches). This inhibits any of the other stinging cells from firing off; prompt medical attention must then be sought. If the victim loses consciousness, resuscitation techniques should be used. Unless the unfired stings have been deactivated with vinegar, no attempt should be made to rub or wipe off adhering tentacles.

There are other hazards that lie in wait for anyone getting to or from a swim. If you happen to be on a coral reef, beware of intricately patterned shells in the shape of a perfect cone. In 1935 in Queensland, Australia, a 27-year-old man handled such a cone shell. He felt an immediate mild stinging sensation in the palm of his hand, within ten minutes his lips felt numb, after four hours he was in a deep coma and dead an hour after that. Cone shells harpoon their prey, usually small fish, with poisonous darts; if we handle these molluscs with bare hands they can sting us, too.

Anywhere along the Australian coast, you may find miniature octopuses stranded in rock pools. When they get excited or annoyed circles of iridescent blue develop on their tentacles and bodies, but beware of picking them up, however much they may look like colourful toys. A bite from a blue-ringed octopus causes nausea, vomiting then paralysis. This can happen within minutes and a victim may soon experience difficulties with breathing. In such cases, first aid to maintain breathing is crucial until the patient can be got to an artificial ventilator.

Stingrays can be concealed on the muddy or sandy bottom of bays. At the base of their tails they have a venomous bony sting with short barbs along its length, which tear through flesh as it is withdrawn. If you've been told they're in the area, avoid stepping on them by shuffling your feet to disturb them as you're wading (the stings are long enough and tough enough to pierce plastic sandals). A stingray victim should put the affected area into a bath of hot water (as hot as they can bear) for 30 to 90 minutes, which denatures the proteins in the venom.

Stingrays are not restricted to salt water, either. I had to use the foot shuffling technique in the Llanos, a swampy region in Venezuela. I'd taken my shoes off for tactile sensitivity because I was feeling for anacondas with my toes. I certainly didn't want my snake hunt to be disrupted by a stingray sting.

I've always been a fan of snakes and whenever I get the chance I actively search them out. There are over 2,700 species, and only a small proportion of these are dangerous to us.

Given the chance, nearly all snakes will disappear into cover when they sense the vibrations from a human footfall. So stamp your feet when moving through snake country. Personally, I walk carefully and slowly so I can see them.

The big constrictors, species that suffocate their prey, rarely attack us; most fatalities are from people molesting them or accidents with captive snakes. Pythons or anacondas that hunt people are figments of the imaginations of Hollywood scriptwriters - our shoulders are just too broad for all but world- record-sized snakes (over eight metres) to work their jaws over to allow them to swallow us.

Venomous snakes can be hazardous to travellers. Boots and thick socks should be worn where they abound. I actively turn over rocks and logs looking for reptiles (I always gently replace them back in the position that I found them in when I'm doing this). I'm always careful not to put my hand underneath or into dark cracks and crevices. While most travellers won't be turning things over, the same rule applies when climbing or scrambling through snake country: don't plunge your hands into chinks in rocks or into hollow logs.

But I've had a close shave myself because of a failure to take common-sense precautions. Camping in Turkmenistan on the Iranian border I had to relieve myself at night. I didn't put on shoes or take a flashlight. When I shone one around the next night I found that there were rodent burrows with saw-scaled vipers laying outside in the sand, next to one of them there was a footprint I'd made the night before. That was a close shave. If I'd trodden on one of these snakes (they are highly venomous and can be irascible) in this remote region, far from medical help, I'd have put my life at great risk.

If I had been bitten, I would have put a compression bandage (this can be made from strips of towel or clothing) just above the puncture wound. This shouldn't block arterial flow and should be loose enough to get a finger between the constriction band and the affected area. The bandage will stop the venom spreading through the superficial veins and lymph vessels. I'd then try to keep calm and rest on the journey as I travelled towards the nearest medical care. In most parts of the world this is usually only a short distance away.

For most travellers the chances of being bitten by a snake are rare. Venom is a complex mix of organic chemicals, usually proteins, which are 'expensive' for the snake to make. Its main use is for immobilising prey and as a method of preliminary digestion. Venom is used in self-defence, but only as a last resort; that's why snakes have developed ingenious warning devices such as a cobra's hood, a rattlesnake's rattle or the bright warning colours of the coral snake. No snake will go after a human being (with one exception, a king cobra guarding its nest, but that would be a rare find indeed), so if you're lucky enough to come across one of these reptiles just stand back and watch. If you're patient, the snake will eventually move. I always marvel at the streamlined design and effortless flowing movement of a snake. If it's close enough or you have binoculars, you can make out its pattern and colour scheme - these can be dazzling. When the snake has disappeared into cover, as it will invariably do, just think for a while about a snake's elegant solution to life without limbs. Snakes will only bite us in self defence, so they should be treated with caution and admiration, not fear and hatred.

Furred predators rarely get as much of a bad press as snakes, sharks or creepy- crawlies, probably because, as mammals ourselves, we feel an affinity with them. Big cats are a potential danger in the tropics (there are some tigers in Siberia, but their numbers have declined so much it would be an honour to be attacked by one), as are bears in temperate or Arctic climates. While it's very unusual for people to be on their menus, there have been cases of rogue lions, tigers or bears that, because of injury or old age, are forced to treat us as food - but these individuals are so rare you've more chance of the plane that's taking you to your destination dropping out of the sky than you have of meeting one of them.

Usually big predators will run when a human approaches them on foot. Accidents tend to happen when they're surprised or when food brings them into close proximity with us. Most travellers will be escorted and/or in vehicles when viewing lions and tigers; but in North America and Russia bears can turn up in many areas - even outside protected parks. I spent two weeks in Alaska's Katmai National Park working on a film about brown bears. I'd never seen these magnificent creatures before, but on encountering them it soon became apparent that they were more interested in the succulent sedge grass and salmon than in us. We always remembered we were visitors to their home, so as we walked along their trails we talked and clapped so as not to surprise them - and, of course, they always had right of way. If they approached us, we'd talk to them calmly, "Hi, bear. Hullo, bear, we're still here," so that hey didn't forget we were there; but if they came to within ten metres or so of us, we slowly retreated.

Campers in bear country shouldn't put temptation in a bear's way. Food should be kept in sealed containers and away from the sleeping areas. Surprising as it may seem, recent research has shown that bears seem to be excited by the odours of menstruation or love-making; so, if possible, a trip should be planned to avoid these from happening when under canvas with bears prowling around outside. The same basic rules apply for polar bears. They can be seen around the town of Churchill in Manitoba, Canada, between July and November, and on the Norwegian island of Spitzbergen in spring.

It's clear that, in most habitats, animals aren't usually a threat to us - but there's just one case where they are - and this is somewhere I'd never venture. The habitat in question is the tropical freshwaters inhabited by saltwater crocodiles (northern Australia and some parts of South-East Asia) or Nile crocodiles (Africa). (If the river or pool was in Africa, hippos could mean a double whammy of danger. There's every chance they'd kill human swimmers, particularly when defending young.) Crocodiles aren't as fussy as sharks about what they attack: anything swimming in their territory is potential food. If I go for a dip in croc country I always check with the locals whether the water I'm entering is really clear of the animals. I don't want to experience becoming prey for an animal that can be up to ten times my size.

So, in conclusion, I think you can probably tell by now that I'd love it if the world were teeming with exciting and potentially dangerous animals, but this really isn't the case. While modern travellers can get anywhere and do anything with relative ease - we hike, camp or snorkel in areas that used to be exclusive territory for animals - when compared with the chances of being harmed by another human being, the danger posed by other creatures is negligible.

The Smithsonian Institute and US Navy have calculated that, right around the world, there are 50 shark attacks each year. During the same period, people in the United States suffer six million dog bites - our best friend causes ten deaths per year. However, there will be under 200 attacks by bears, sharks, crocodiles and alligators, with fewer than ten deaths. Snakes bite 3,000 people in Australia every year, but 90 per cent of these bites are from non-venomous species. Medical care and anti-venom treatment are so efficient nowadays that, even among the 300 or so people who are actually envenomated, deaths are extremely rare.

In most situations, all that's required to avoid a bite or attack is an awareness of the presence of animals that could be a threat. No creatures show malice aforethought, we just need to be careful and not blunder into a curtain of jellyfish tentacles or tread on a camouflaged viper. If we keep our eyes skinned and senses alert, an encounter with a predator can be one of the most thrilling and memorable experiences of our lives.