I think the problem with a lot of people in this thread is they don't know what real fighting looks like.
MMA may look like brawling but that's what it looks like when 2 skilled fighters compete. What are you expecting? Spinning hook kicks, dragon punches and hadookens?
What you see in the movies isn't fighting...
Anyway, Bruce Lee was very skilled. If he trained MMA I have no doubt he would be very good at it however, he didn't train MMA so would not fair too well.
*Edit - Also Bruce Lee wasn't a fighter. Demonstrating a crazy quick punch and effectively using the same punch when you have an opponent trying to take your head off is very different.