1. There she blows: Whale-watching
It's a heart-stopping moment: a distant spout breaks the horizon and your boat changes course. In the blink of an eye the vast, apparently empty ocean has come alive.
Since watching whales has for most nations overtaken hunting them (with a few shameful exceptions), the populations of many cetaceans have bounced back. Humpbacks, once hunted to near extinction, lead the charge. There is reliable viewing everywhere from the New England coast to the Mozambique Channel. This species often approaches boats and puts on a show, with impressive breaching and tail slapping.
These migratory animals make seasonal journeys between their mostly polar feeding grounds and equatorial breeding quarters. Hot spots include the Sea of Cortez for grey whales, the Azores for sperm whales and Sri Lanka for blue whales. And the delicate of stomach need not even set sail: the southern right whales that calve in the shallow bays around South Africa's Cape offer superb land-based sightings.
*Naturetrek offers a 14-day whale-watching and wildlife holiday in western Mexico, including an 11-night cruise down the west coast of the Baja Peninsula and into the Sea of Cortez. Prices start at £3,695 per person, including international flights (01962 733 051; naturetrek.co.uk).
2. The thunder of hooves: Serengeti/Masai Mara migration
For a moment the frontrunners hesitate. But then, pressed forward by the massed ranks behind, they take the plunge. The dam of bodies breaks in a torrent of dust and hooves as wildebeest thunder by the thousand into the churning brown waters of the Mara. Bobbing heads strike out in wild-eyed desperation for the opposite shore, and the crocodiles – who have waited months for this moment – slip into the current and cruise towards the melee.
Not for nothing did Basil Fawlty ask the unfortunate Mrs Richards, when she unwisely requested a room with a view, whether she'd expected "herds of wildebeest sweeping majestically across the Serengeti plains". East Africa's great migration, in which zebra and gazelles join Africa's most lugubrious antelope in a two-million-strong gathering of grazers, consistently tops the polls for the planet's most impressive wildlife spectacle. From a distance the herds seem arranged to emphasize the sheer scale of the landscape. Up close you are immersed in a world of munching and grunting – punctuated by carnage, as lions, hyenas and cheetahs move in to claim their share.
*Wild About Africa offers a 10-night camping safari to Serengeti in Tanzania, also including Lake Manyara and the Ngorongoro Crater. Prices start at £2,672 per person, including international flights (020-8758 4717; wildaboutafrica.com).
3. Going ape: Africa's gorillas and chimps
Don't expect chest beating. The most you'll get from the silverback may be a clearing of the throat and the muffled report of breaking wind, as he rolls over onto his immense stomach. But nothing, not even Attenborough's most famous moment, prepares you for the musky intimacy of sitting among a troop of mountain gorillas in their dripping forest. Or that sense of connection as a mother, snatching up her infant, catches your eye before settling back into the undergrowth.
With chimpanzees, an even closer relative, it's an altogether different experience. Whoops, shrieks and crashing from the canopy reveal their presence long before you see them – sometimes leading you in a breakneck scramble along dense forest trails.
*Rainbow Tours offers an eight-day private tour to Uganda, including chimp (Kibale) and gorilla (Bwindi) tracking, plus other Ugandan wildlife highlights. Prices start at £4,194 per person, including flights from the UK and gorilla permit (020-7226 1004; rainbowtours.co.uk).
4. Polar horizons: Arctic and Antarctic
A trail of paw prints leads to the butchered carcass of a ringed seal, smeared in scarlet across the frozen white. Their author, a huge polar bear, lifts his muzzle to sniff at your approaching Zodiac, scattering a posse of protesting glaucous gulls. Behind looms a tableau of improbable perfection: fissured glaciers stretching back to the fantasy pinnacles of Svalbard (known to us as the Norwegian archipelago of Spitzbergen).
At the bottom of the world another icescape assembles different players: the clamour and jostle of emperor penguins huddled after their long trek from the interior; the fishy exhalation of a leopard seal, cruising the ice edge in search of the unwary; giant petrels slicing the frigid air, sniffing out carrion.
Ice would not seem the most promising natural habitat. But the frozen backdrops of the Arctic and Antarctic make for dramatic wildlife encounters. Fertile seas fuel a rich food web that supports some of the hardiest creatures on earth.
*Exodus offers an 11-day Svalbard cruise in the Arctic to/from Longyearbyen, with prices starting at £3,930 per person (June–August). It also has a 15-day cruise to the Antarctic Peninsula, to/from Ushuaia in Argentina, from £4,130. International flights are not included (0845 330 6013; exodus.co.uk).
5. Tropical waterways: Brazil's Pantanal
You hardly need leave your lodge. Sheep-sized capybara nibble the lawns, caiman sprawl beside the ditches and hyacinth macaws flap raucously over the terrace. The variety of Pantanal life is startling – and it's all so much more visible than behind the Amazon's dense veil of green.
Hit the trail at dawn, to the roar of howler monkeys, and you meet agoutis pitter-pattering over the leaf-litter and marmosets leaping through the canopy. Take to the river in the late afternoon and you find green iguanas draped across the overhanging foliage and giant river otters cavorting around your boat. This is also the best place in South America to glimpse a jaguar. Fingers crossed as you comb the riverbank for spots.
*Wildlife Trails offers a one-week privately guided Pantanal tour to/from Cuiaba, Brazil, including four days of private boat safaris. Prices start at £1,450 per person, excluding international flights (0844 686 5532; wildlifetrails.co.uk).
6. Evolutionary inspiration: Galápagos Islands
This remote Ecuadorian archipelago is synonymous with Charles Darwin and evolution. It was a bunch of apparently unremarkable birds he found here, now known as Darwin's finches, that fuelled the great scientist's theories.
The islands themselves have evolved since Darwin's time. Sadly, not for the better. Invasive flora and fauna have played havoc with vulnerable native species and, more recently, unchecked tourism has battered the fragile environment. Nonetheless, visited responsibly in the hands of a reputable tour company, this remains one of the world's most extraordinary wildlife destinations.
Attractions include giant tortoises, marine iguanas (pictured), comical blue-footed boobies and flightless cormorants. And then there are the hammerhead sharks and striped dolphins that ply the sparkling reefs and blue depths offshore.
*Responsible Travel offers tailor-made eight-day Galápagos cruises by yacht with a qualified naturalist from £1,999 per person, excluding flights ( responsibletravel.com).
7. Weird and wonderful Down Under: Australia
Millions of years of evolutionary isolation has produced a unique fauna in Australia, with the likes of kangaroos, koalas, platypus and echidnas found on no other continent. And it's not just the mammals. From frilled lizards to cassowaries, weird wildlife lurks everywhere. What's more, it's easy to find, with roos grazing near many towns. Try the north-eastern rainforests for cassowaries, and Tasmania for wombats, wallabies and echidnas.
*The "Western Wildlife Experience" offered by Intrepid Travel is a 10-day journey from Adelaide to Perth that will introduce you to kangaroos, wombats, emus and dingoes. The price of £850 includes transport and accommodation but not flights (020-3147 7777; intrepidtravel.com).
Closer to home
Europe may have tamed much of its wilderness and eradicated most larger beasts, but there remain some outstanding wildlife experiences just a family holiday or city-break away.
Highlands and islands
North-west Scotland is Britain at its wildest, with teeming seabird colonies and rare wildlife such as eagles and pine martens. Mull is the jewel in its wildlife crown: both golden and white-tailed eagles breed here, otters forage along the shore and basking sharks cruise the sheltered bays. Take a summer boat trip for porpoises, puffins and perhaps even a lunge-feeding minke whale.
The Pyrenees change character dramatically from the forested French slopes to the wild crags south of the Spanish border. This is raptor central, with eagles, kites, griffon vultures and rare lammergeyers soaring above flower-studded hillsides. Hike into Ordesa National Park for chamois perched on precipices and wild boar rooting in the meadows.
Brown bears still roam the remote Nordic forests, and Finland is the best place to see them, with hides to make life easier. Other mammals here include huge elk, nocturnal flying squirrels and – for the very lucky – shy lynxes and wolverines. Birders can enjoy such northern forest specials as the great grey owl and the black woodpecker.