Please pardon if I accidentally restate something that has been previously said, I have foolishly not taken the time to read ALL of the replies yet.
I have been working on a similar project, but instead of a quadrotor, I'm building an ROV (underwater). Basically, MOSFETS are the way to go for a small, compact yet extremely powerful speed controller. Here is a video that helped me a lot in understanding MOSFETS that I hope will help you. I strongly recommend checking out the other videos in the series; they are very valuable and well thought out electronics tutorials.
http://www.youtube.com/watch?v=CFt8h...ACE&index= 26
If you use MOSFETS, you need a snubber diode and really should have some capacitors for decoupling and signal noise reduction. You should use a tiny ceramic cap for very fast reactions paired with a larger electrolytic cap to handle the large loads.
I can send eagle files/circuit diagrams if that would help, just pm me.