HIV is spread through contact (directly) with an infected person's bodily fluids. If a mosquito sucks the blood of an HIV positive individual, it won't transmit to another human. The mosquito would use it for other things, as Chewed Bubblegum mentioned. In addition, HIV needs specific T-cells in order to replicate, and luckily, mosquitoes (and other blood-sucking insects) don't have these cells. Ultimately, the virus is broken down. A LOT of people would have HIV/AIDS if not for this!
Thank God for AP Biology.