Hard to say. Mosquitos, is probably not one of them because even as much as we hate them, many animals prey on them, so unless other insect replaces them as a food source for those animals, them disappearing would probably affect many other species and subsequently, other species that may feed or depend in some form on those that feed on mosquitos.
My answer would probably be ticks, since I don't think there's many animals that feed on them and their only usefulness is population control, which should be doable by other species either way.
Edit: bed bugs as well, since it was mentioned by other commenters, I hate those fuckers and last I checked they weren't any animal's primary food source.
I remember reading some scientic article that examined what would happen if we eradicated the mosquitos entirely.
Surprisingly, they came to the conclusion that they'd just be gone and we would be a lot happier without the nuisance and the diseases they spread.
No other species is dependent on mosquitos as a food source, they could easily find enough to eat with them gone. Mosquitos apparently serve no known vital purpose in their ecosystems, although it was mentioned that males of some species have some little value as secondary pollinators.
That's interesting. With how many of them there are and knowing that many species eat them, I would have expected that at least some of them would suffer in some way.