Combat just takes too long in 3.x and 4E.
The extensive rules for implications of movement on the battlefield, and the focus on the visual combat grid are, in my opinion, the main problems for speed. The problem is, I love the grid and the rules for movement on the battlefield - I just hate the time it takes to resolve encounters. How do you keep the options and shorten the time? No idea.
easy. eliminate attacks of opportunity rules and any combat move whose result may create one for either side of the combat.
eliminate flanking rules and anything to do with giving any bonuses to anyone for flanking, including eliminating giving thieves the ability to flank and backstab in battle.
eliminate every combat move other than swinging a weapon at someone. this means eliminating trip, grapple, and all the rest of those listed in the combat section.
lastly, give one attack per round to everyone except fighters who get 2 at 10th level.
that ought to do it. we have implemented all of those rules in our game except the one giving everyone one attack per round, and our combats are faster than most i think.