I have all three. Pros/Cons of each:
PS3
Pro:
Some great exclusives which can't be found on any other platform (Little Big Planet, Infamous, God of War, anything Pixeljunk, Fat Princess, etc.)
Online play is free
The PSN store titles are generally affordable and quoted to you in dollars/cents so you know exactly what's being spent
Bluray player.
hard Drive can be easily changed/upgraded at user level with no gimmicks, and very affordable.
Bluetooth means easy access to a range of periphials, especially for mic/headsets.
Con:
Unlike the XBOX360, there is a very minimal number of demos and the store seems very limited in comparison. VERY.
Some exclusives of course will be missed if on other platform (true of all)
Limited title base in comparison.
XBOX360:
Pro:
Tons of exclusives thanks to MS's pockets; and if a title is on both PS3 and XBOX360, the XBOX360 version will normally have much easier access to Downloadable content (see: GTA3)
In depth storefront, with community games and small minimal cost items, tons of demos.
Compared to PS3, relatively fast load times per title, the ability in new versions to copy disc to HDD speeds that up.
Direct integration with MS Media Center as an extender, etc.
High profile exclusives
Con:
Most dated of all the generation of hardware, so some functions are simply not viable; MS bet on HD-DVD.. and lost, and has no plans to adopt BD.
Even though they keep redesigning, the thermal control in the units is still wrong. Which means red ring of death is still not a thing of the past.
Exclusive titles on other platforms.. etc. etc. etc.
Wii:
Pro:
While other consoles are adding motion control, since it's "in the box" on wii, almost all titles have access to it. Developers for motion control on Sony/XBOX will be appealing to a much more limited audience, because it has to be someone who has both the PS3/XBOX and the add-on, which means fewer games to take advantage of those functions.
Generally light, quick play games which are best played in groups; if you are into large local play, Wii for sheer "fun factor" is a real contender.
If you're a fan of Guitar Hero, etc. let me make a case here.. I have it on all three platforms (I know), but nothing, on any platform tops GH5 on Wii. By far, the most fun version of that game, anywhere.. with modes that aren't available anywhere else, and wow does it just work. I play it and then go back to the PS3 for Rockband and miss it :)
Nintendo First party exclusives. Don't knock it. Access to Nintendo's vast library is a huge plus, and for people who are oldschool gamers, it's a chance to go back and find things out of their childhood. My kids play more "Legend of Zelda: A Link to the Past" then any other game I have on any console.
Wii Store is generally affordable with some great titles.
Cons:
Online Play is virtually non-existant with few exceptions.
Display is NOT HD (480P at top via component)
Storage space in Wii is beyond meager, meaning you may rotate in and out games you have bought using SD cards
I like each of them on their own. But find what works for you. I'd say this of the XBOX360/PS3: If you're getting one, do the right thing and make sure to get the newest revision. For a PS3, that's a slim. For an XBOX360, that at this point should be everything on the shelf. Older units of both all had minor to major issues with stability and lifespan. Newer versions correct that.