Additionally, attacks of opportunity are not new; in 1E, etc. (IIRC), characters would get a free attack at enemies who disengaged from melee combat.
AoOs are an extension of that same philosophy - that when someone is in your face with a sword, you darn well better pay attention to them - expanded to other aspects, as well.
Moreover, they provide a mechanical method to enforce the capability of fighter-types to stand in front of and protect "squishier" characters behind them. In earlier editions, it was always understood that it was the fighter's (etc.) job to protect the wizard. It just was not particularly clear how, apart from camping out in a doorway, that was possible. Nothing, apart from DM largesse, prevented an enemy from just walking past the fighter to beat up on the wizard.
Now, at least, the fighter has a zone of control wherein he can at least make an enemy think twice about ignoring him. 4E, IMO, does this even better.