Earlier quoted context omitted.
It'd be sort of like removing all of the kelp from the worlds oceans. It'd have ripple effects on other species that we wouldn't want to negatively affect.
People have studied this. While you have to take these theoretical "what if" studies with a grain of salt, some believe that eradicating mosquitos would not affect ecology in a major way: http://www.nature.com/news/2010/100721/full/466432a.html
I've gotten malaria on a trip to west Africa, I've had to get yellow fever vaccines, i grew up in areas with west nile, etc I understand the impact it has on humans. However, there is more to the mosquito than the little insect flying around biting us. Their eggs and larvae play a huge role in the ecosystems they inhabit.