I can barely get to sleep because some misbegotten mosquito decided to go to town on me.
Creatures like spiders or bats I can deal with because they do good things but mosquitoes? Do they have any other purpose because making people miserable?
If not, humans seem pretty good at extinguishing any number of species, what is it about these fu***** that make them so impossible to eradicate?
For one thing, they feed the bats.
Blame Noah and his family. They had the chance to not take them on board, but Noooooo.
Just a couple weeks ago, I heard someone discussing the bee die-off who mentioned in passing that among the alternate pollinators were mosquitos. So I guess they have some use. It occurs to me that the only nitrogen source that bees have is pollen.
The huge Spring migrations of birds to the Arctic to breed and raise their young are very dependant of the ample supply of mosquitos as a food source.
The mosquitofish (gambusia affinis) is quite partial to mosquito larvae.
Mosquitos are important food items for many species of birds like swallows and purple martins, bats, and especially dragonflies, which are the mosquito hunters of the insect world, and as such, form an important part of Earth’s ecosystem.
As for “why can’t we get rid of them?”, it’s because we as a species don’t want to badly enough. We could basically nuke every potential mosquito habitat with a wide array of pesticides and habitat modification, if we wanted to (think “paving and/or draining the entire state of Florida, then dousing it with insecticide”), but the tradeoff would be the poisoning, ruination, and total desolation of Planet Earth, since many other species would also perish, all the way up and down the food chain.
Seems kind of a steep price to pay for a few skeeter bites. 
I suppose someone could, if they wanted to, come up with hormone-based mosquito control the way they came up with flea control and roach control, but as mentioned, mosquitos are an important food item for many other species here on Planet Earth. If you were to spread some kind of mosquito hormone control around your scenic pond next to your house so you can sit on your deck in the evenings without being eaten alive, all your barn swallows, and the martins whose house you so carefully put up, will move elsewhere, as there’s nothing for them to eat. You also won’t have any dragonflies after a while, but not everybody cares about that. 
And since mosquito larva also constitute an important food item for fish, pretty soon you’ll start noticing that you don’t seem to have as many sunnies in your pond as you used to…
Calamine lotion works well, BTW. Shake the bottle really well for a couple minutes, dab it on with a cotton ball, let dry.
Dragonflies live on mosquitos. And dragonflies are cool. So I guess we have to leave the mosquitos in place.
Drat.
Another problem with eradication is that it is a world wide problem. The mosquito that bothered you was probably an Asian Tiger, a particularly nasty, never give up, quick on the draw bug that first showed up in Houston, Texas in tires from overseas and has continued to spread ever since.
There are reports that it’s on it’s way to the UK. I’ts already been seen in continental Europe.
Then whoever started the Pit thread about the cold weather in GB had best be counting his blessings. The Asian Tiger should be the one exception to another reason why eradication is difficult, mosquito huggers.
And I thought this thread was a tribute to The Mosquitoes (Bingo, Bango, Bongo, and Irving). Darn.
Where did you get the idea that every single creature on the planet must have a “purpose,” or it should be exterminated? What’s your purpose?
I wondered that, too, at first, but upon reflection I realized that the OP must have meant, “What is the mosquito’s place in the ecosystem?”
Seriously though, have we not reached a point in biotechnology where we can eradicate a species at will by tampering with their genes/reproductive abilities? If not, we need to prioritize this, and in the meantime allow mosquitoes to head the shortlist of test species.