Almost everything I have to say has already been said. Better (and customisable) controls, better graphics, exclusive games, $10 cheaper, mods, only good platform for RTS's ect.
But what people don't always mention is that once you build your own gaming PC it becomes a learning experience, a skill, and often a hobby. It isn't just the games, but the expirience itself of building, upgrading, and comparing you rig.
I'd be more then happy to help you in building your own rig, wheather you need part recomendations, questions answered, or abit of tech support. Send me a PM if you want.