What is the purpose of crocodiles or mosquitoes?

Great question! In some instances, local wildlife can pick up the slack, especially if it was an introduced species that went extinct. Unfortunately, that isn't usually the case. Most of the time there is nothing else able to branch out quickly enough to cover the damage :(

What is the purpose of parasites?

Usually in an ecosystem, if one animal dies out, then many others will too. Take Yellowstone Park for example. IN the past century, hunters have killed almost all of the wolves in the park, because they were stirring up trouble for the other inhabitants (sheep, deer, people, etc.). WHen the wolves died, the deer population grew, and when it grew, it over-grazed the grass that was growing near Yellowstone River. Since grass keeps soil from eroding too quickly, the lack of grass caused the river to die out and spread, but today's scientists have saw this and have fixed the ecosystem of Yellowstone by force migrating a pack of wolves into Yellowstone Park. After the wolves came in and settled, deer population was in check, grass grew, and the river stopped eroding. That was an example of a missing link is a food chain, but Yellowstone's food chain was a bit weak and relied too much on the population of wolves. However, with stronger ecosystems with mroe diversity of plants and animals (I.E: Rainforests), a food chain does not exist, but a food web. If one producer or tertiary consumer dies out, another wil take it's place. The end of life you talk about may not be so drastic in one area, but it may be very possible in another area.