So to summarise:
Why a PC:
1) Much better graphics if you're prepared to spend out on upgrades every so often.
2) Vast library of titles availiable even going back to the dawn of computer gaming with emulators and virtual machines.
3) Enthusiast grade PC's are a fun hobby in themselves.
4) The games are cheaper & if you're of that inclination piracy is easier.
5) You have the option of mouse & keyboard which owns for FPS, RTS, RPG. (A major concideration if you're a fan of one of these genre)
Why a console:
1) You can slouch on the couch in front of the TV to play games rather than sitting at a desk.
2) Its easy and fun to have a few mates round and play against each other.
3) Consistent gaming experiance as the hardware is identical.
4) The console itself is cheaper than a Gaming PC and won't take up the same room, suitable for a casual gamer.
I haven't included any of the points people raised about using computers for non-gaming activities because to be fair you don't need an expensive gaming PC for those things, a cheap laptop would do fine. Although of course you can do those things on a Gaming PC and you can't on a console so I suppose that is a vaild point from that perspective.