Meet, if you dare, the Old World hookworm. Its flesh is a pinkish grey, and its head is slightly, creepily bent away from its body. It has a wide mouth, almost as big as the entire head, barbed with two pairs of sharp teeth. It looks like a finger with the jaws of a great white shark. And it is a parasite.

The Old World hookworm lives in the intestines of bigger animals, including many humans. It latches onto the wall of the intestines with its teeth, and sucks its host's blood. In this way, the hookworm prospers at its host's expense. Like all parasites, it takes and gives nothing back.

Surely we would be better off without such a good-for-nothing drain on resources? Suppose all the world's parasites disappeared overnight. Wouldn't all the other animals be healthier, and wouldn't there be less suffering? Surprisingly, a world without parasites might not be a nicer one. There might be just as much sickness and pain, but much of the beauty of the natural world would be obliterated. Perhaps worst of all, we might all stop having sex.

There are millions of different parasites. The word is derived from the Greek word "parásītos", which means "one who eats at the table of another". They infect and live off other species, known as hosts, benefitting at the expense of their chosen victims.

Around 50% of all organisms are parasitic

It's not just worms: many groups of organisms have some members that are parasites. Plenty of fungi are parasites, including the largest living organism on Earth, a honey fungus 2.4 miles (3.8 km) across in the Blue Mountains in Oregon. There are also parasitic plants such as mistletoe, not to mention fleas and lice, and viruses and bacteria. There are even bird parasites: cuckoos are the most famous, thanks to their cheeky habit of laying eggs in other birds' nests.

Scientists estimate that around 50% of all organisms are parasitic. "There's a huge universe of parasites," says parasite expert Andres Gomez of ICF International in Washington, DC. "They are abundant, ubiquitous, diverse and important."

Clearly, if we got rid of all the parasites, the world would look very different. You would notice the difference before the first day was out.

"Within hours, millions of poor people would be cured of serious chronic illness like malaria, schistosomiasis and ascariasis," says Kevin Lafferty of the US Geological Survey in Santa Barbara, California. "People would be able to work harder and enjoy their lives more. Their livestock and crops would be healthier too."

Our immune systems have evolved to cope with a certain amount of infections

But this honeymoon period wouldn't last long. For one thing, our bodies might rebel against it. "There could be unanticipated consequences of taking parasites away, because we've been co-evolving with them for so long," says Jaap de Roode of Emory University. "It wouldn't be good for us."

According to the "hygiene hypothesis", our immune systems have evolved to cope with a certain amount of infections. So if we aren't exposed to parasites and other diseases when we're young, our immune systems don't develop properly and can start attacking our own bodies. This may explain why so many people today, living in clean environments, suffer from allergies and autoimmune diseases. If we weren't exposed to any parasites at all, we might suffer from even more of these diseases.

What's more, it wouldn't just be our immune systems that ran out of control.

As well as harming people, parasites keep down the numbers of plant-eating insects and other animals we consider pests. Within months, these species would increase in numbers and cause serious damage to food crops, says Lafferty. As a result, we would have to use even more pesticides, which would affect wildlife. Even with the extra pesticide, "some people would start to go hungry," says Lafferty.

We'd have to kill a lot of things

"Almost every species you can think of has a parasite," says Levi Morran of Emory University in Atlanta, Georgia. "And parasites have a role in ecosystems to cull populations and keep them in check. Without parasites, populations could explode."

Without parasites, we would have to start culling species whose numbers would otherwise explode, says Morran. "That would be difficult and something humans haven't dealt with before," he says. "We'd have to kill a lot of things, so it would be rough."

And it wouldn't just be us doing the killing. There would be a cornucopia of animals and plants, that in the old world would have been killed as a result of their parasites. Something would have to eat them.

"Nature really doesn't like a vacuum," says Lafferty. As a result, predatory species like spiders and birds would take the place of the vanished parasites. Over the years, these predators would become more numerous, and in the long run more would evolve.

This increased threat from predators would transform many animals and plants. After a few centuries, Lafferty says, evolution would change the "types of defences that animals and plants invest in: more spines, thicker shells, distasteful chemicals."

One possibility is that the oceans would turn into thick green mats

It's not clear what this would mean for ecosystems as a whole, but it might well be bad news. "These food webs might be more or less stable - we are just starting to sort this out - but my guess would be less stable," says Lafferty.

The changes could be particularly dramatic in the oceans, says Luis Zaman of the University of Washington in Seattle. The seas are filled with algae and other microorganisms that get their energy from sunlight. Directly or indirectly, they feed all the animals in the sea. But they are "constantly battling viruses," says Zaman, and that keeps their numbers down.

"Without these viruses, it is hard to say what exactly would happen," says Zaman. "One possibility is that the oceans would turn into thick green mats, like the ones you see on small ponds by the road."

This would be bad news for everything else in the ocean. "Take out all of the parasites across the ecosystem, and it probably will collapse," says Zaman. "It might take a while, and it might oscillate wildly between states of lush vegetation and barren desert, but it almost certainly wouldn't end well."

As well as helping keep populations in check, parasites have a longer-term effect: they power the evolution of new species. Yes, really: we have parasites to thank for much of the diversity of life on Earth.

That's because hosts and parasites are in a constant evolutionary arms race, which pushes both of them to get better at surviving. "When hosts and parasites interact it's really fertile ground for co-evolution," says Morran. "This host-parasite co-evolution is responsible for a massive amount of evolutionary change in the history of life on earth."

We would see even more drastic rates of extinctions

In research published in 2014, Zaman simulated the evolution of organisms using a computer model, and found that parasites force their hosts to become more complex. When he suddenly removed the parasites, the host animals became much less complex, and much more alike.

In real life, Zaman suspects that removing parasites wouldn't just make other organisms simpler. "My bet would be that we would see even more drastic rates of extinctions," says Zaman. "Research has shown many times that parasites are important drivers and maintainers of diversity."

They also may have driven animals to become more sexually attractive to potential mates.

There is no courtship ritual finer than that of bowerbirds. Found in the forests of New Guinea and Australia, male bowerbirds make beautiful works of art to attract a mate. They construct a bower from sticks, and decorate it with brightly coloured objects like fruit, shells and even man-made objects like pens. Females will only mate with them if their bower is of excellent quality.

There is a theory that the evolution of this extraordinary display was driven by parasites. The same goes for other awe-inspiring sexual attributes, such as the dramatic tail feathers of a peacock, the great mane of a male lion and the theatrical horns of a ram.

Dramatic male traits like a peacock's tail are a kind of badge of honour

In the early 1980s, W. D. Hamilton and Marlene Zuk studied the sexual displays of North American birds. They found that species that were more prone to blood parasites tended to be showier: males and females were both more brightly coloured, and males were better singers.

They suggested that dramatic male traits like a peacock's tail are a kind of badge of honour. They are a message to females that this male has fought its parasites successfully and still has energy to spare. A female ought to choose a male with these extreme traits, because it suggests the resulting offspring would inherit his ability to resist infection.

The same might be true of sexually-attractive traits in humans, says de Roode. "Some people think the brain we have to create music, or even the ability to think about biodiversity, may be the result of sexual selection - of which parasites are believed to be a main driver."

As well as driving the evolution of flashy courtship, parasites could be the main driver for the very existence of sex in the first place. The main benefit of sex is that it shuffles genes, allowing animals to produce offspring quite different from themselves. Parasites may encourage this rapid genetic turnover by forcing hosts to keep evolving.

This idea, that animals must keep improving their design just to stay alive in a competitive world, is called the Red Queen hypothesis. It was proposed by evolutionary biologist Leigh Van Valen in 1973. Van Valen named it after a passage in Lewis Carroll's Through the Looking Glass, in which the Red Queen tells Alice that in the novel's alternative world "it takes all the running you can do, to keep in the same place".

Males might even become obsolete

There is experimental evidence that sex helps animals survive parasites. In 2011 Morran showed that infectious bacteria could wipe out populations of asexual worms, whereas worms that did have sex survived.

So if parasites drove the evolution of sex, would getting rid of parasites stop species having sex? It's not out of the question, says Morran. "If we took away parasites we may be in a situation where asexuality becomes prevalent." Smaller species would stop far sooner, he says. Humans are so hard-wired to mate it would take a long time for us to become asexual or self-fertilising. If we ever did, we would become more genetically alike.

Humans would be transformed as a species if we stopped having sex. Males might even become obsolete, says Lafferty. "In areas where parasites are rare, male snails start to disappear from the population, leaving females that can reproduce on their own," he says.

So far from trying to eliminate parasites from the world, some scientists are now suggesting that we should conserve them, just as we take care of pandas and tigers. On the face of it the idea sounds ridiculous, but Gomez believes they are worth saving. In a paper published in 2013, he argues that parasites can organise ecosystems, and that often one parasite will protect its host from another more harmful parasite.

Who would donate money to save the rhinoceros bot fly?

They could even be useful to medicine. Viruses are a kind of parasite, and many of them use bacteria as hosts. So if a person has a bacterial infection, the right virus could be used to treat it – rather than standard antibiotics, which have been massively over-used. At the moment such "phage therapy" is only really used in Russia, Poland and Georgia, but other countries are now taking it more seriously. The US National Institute of Allergy and Infectious Diseases recently announced plans to use it to combat antibiotic-resistant bacteria.

Parasites are threatened by many of the same factors that affect other species: things like climate change, pollution and the destruction of habitat. Nevertheless, conserving them is not an easy sell. Who would choose to donate money to save the rhinoceros bot fly, a massive insect whose young develop in the stomachs of rhinos, when they could help save the rhino instead?

It's a problem conservationists are going to have to face up to. In the meantime, if you're still tempted by the idea of a world without parasites, you might want to consider that it wouldn't stay that way for long.

Instead, new parasites would probably evolve almost immediately. "There is so much to be gained from being a parasite," says Morran. "I would predict that if you snatched all the parasites away, it wouldn't be long before other species moved into those niches."