I have the PS3, XBOX 360 and Wii (actually two Wiis). I use our PS3 as a BluRay Player (I own 3 or 4 games for it, that's it). I'm not a huge fan of the Dualshock controller. Don't get me wrong, i don't hate it, but i like the XBOX Controller better.
I use the Wii for fun, light-hearted, and very enjoyable gaming. I LOVE the mario, zelda and DK series, but the Wii also has the new Goldeneye, Epic Mickey, tons of other First Party games that are a blast to play, especially with my wife who doesn't generally game much (she enjoys Epic Mickey, Kingdom Hearts, DK and the mario games, but that's about it discounting any 'party' games. I find the Wii to just be a ton of fun, and while I still manage to get sucked into the games, i don't get as frustrated with them as i do with games on the other systems.
I know the xbox hasn't come up as seriously in the topic, but to be complete: I use my XBOX for more 'serious' gaming (CoD, Fall Out, Halo reach, etc...) but also some of the more 'fun' games that are available thanks to Kinect. I vastly prefer XBOX Live over PSN, personally. I vastly prefer the interface of the XBOX Live marketplace (and the dashboard as a whole, versus the XMB) and the achievements work better than the trophies (come on, syncing the trophies?) Plus I just have more friends on XBL than PSN.
If I didn't own any of the consoles, but my Wife and I were looking, I'd probably wind up buying a Wii thanks to the gaming library. My wife and I grew up with NES/SNES games, so that's a pretty huge factor (because I grew up playing and loving the classic nintendo series' and thus have a bias) but also because my wife isn't a huge gamer, and many of the games are a bit more approachable for her to play on her own and for us to play together. Online gaming isn't terribly important to me, I still like the idea of playing together in the same room, so that's also a factor worth considering. Of course, the Wii's graphics are FAR from the best, but is something worth considering. For me the graphics aren't something that's ever been much of a factore since I find that it's far more important to have fun playing.