This is a question that, although not very important, has come up time and again. I personally prefer the spelling mosquitos, while others (including my spell check) like the spelling mosquitoes.
Mosquitos were not always referred to by that name. Native Hispanic Americans called them zancudos, which means "long legged". The English preferred the term gnats, while the French called the either Les cousins or Les moucherons. The Germans, like the french had 2 terms commonly used, stechmucken or schnacke. To Scandinavians myg and myyga referenced the pest. Going back further, the Greeks referred to mosquitos as konopus, while Aristotle, the Greek philosopher, used the term empis, in his recorded studies of animals.
To answer this question correctly, I believe we need to go back to the origin of the name we give this bloodsucker, mosquito. The mosquito gets it's name from the spanish phrase meaning "little fly". "Mosca" meaning fly, and "ito" which means little or small. The name solidified in the late 1500's, and became the common name for the group of insects in the Culicidae family.
The final determination is that both spellings, mosquitos and mosquitoes, are correct!! In spanish the spelling would be mosquitos. If someone decides to add an "es" to the end, as many words in english do, it would also prove correct. The simple answer would be that you're right!!!!