I have all three and each has it's own place in my home. The Wii is VERY fun with multiple people; especially if you get Wii Fit. There is also the ability to download olf NES, SNES, Sega, Genesis, etc games and play them there. The Mario games are awesome and it has free online play with games like Mario Kart and GoldenEye. The PS3 is great because it doubles as a blu-ray player and they all have built in Wi-Fi (minus the original 20gb) so streaming Netflix movies is easy and high-def unlike the Wii. I have an original 60gb system so it has hardware playback of PS2 games which is also really neat but you have to drop serious coin to get an old 60gb. The Xbox has the best lineup of games and Kinect is really cool also. I've never had any trouble with my 360 and I've used it a lot and for long periods of time. That's my .02 on the issue.
Cliffnotes:
Wii = Fun for lots of people
PS3 = Great multimedia system
360 = Best game selection.