D&D will always be slow, and dumbing it down like that is not the answer. 4th edition rules have "minion" enemies that only need 1 hit to kill, and they do make for some interesting encounters.

Me? I made my own rules. What really made things feel fast is that everyone takes their turn at the same time. Not only does this prevent everyone from awkwardly waiting while everyone contemplates their turn, it also lets everyone discuss their next turn together and actually use strategy instead of independently respond to threats. I did this by making cards, and everyone plays their card at the same time. There was a "speed" stat that determined who actually got to attack and move first, and combat advantage was completely reworked to allow for "moving duels" like you see in the movies. It wasn't very balanced, but everyone was very impressed with the flow of combat.