i have all 3 systems and for some reason i have more ps3 titles than anything.
im not really big on console gaming as i was and im more of a collector now. however i can give some insight of what i like about each.
starting with the wii. the wii sports and the like are fun games to play with a group of friends but if you dont have friends (

) then it doesnt shine as much. beyond that i like all of the traditional nintendo franchises and if you like them as i do and want to continue to play them, you need a wii. mario, zelda, smash bros, etc. also note that you can play gamecube games on the wii but you will need a gamecube memory card and controller. the virtual console offers several games from the past, including nes, snes, genesis, turbo graphix, neo-geo. note any games you download from the virtual console are linked to that system. there is no true network account as there are with the other systems. through homebrew, which is a way to customize your wii, you can enable dvd playback and a number of other things.
xbox 360, is a decent gaming hardware. i havent had problems with mine. the older model, cant speak for the newer slim model, will scratch your dvds if the drive is ever moved while speeding. how badly depends on how badly you tap it. that is one design flaw of it. xbox live has ton of features however you have to pay to access many of them. they are more seamline then the other consoles but again, you pay for them. i stopped playing online so i canceled from xbox live.
ps3, i have the older model which enables me to play ps2 games. i do that more often than not. ps3 uses psn which is like xbox live service. psn use is free however there is also a paid version called psn+. psn+ offers a new of additional features including free game downloads. psn is functional but in my experience slower than xbox live. however you dont have to pay to play online unlike with xbox live. sony also offers movie downloads and rentals. being so closely linked to many of the movie studios, they have a larger selection than what you will find on the xbox, xbox does have the zune marketplace.
all-in-all, the 360 and ps3 offer very similar gaming experiences. many of the titles are the same, many of the features are the same. both can be used as a media hub. the biggest difference and plus is the inclusion of a bluray drive on the ps3. there is HD content available for both streaming and download on each system but they do not compare to BD.
which one to buy? if you like nintendo franchises, you have to buy a wii. 360 and ps3 being pretty much the same gaming experience you have to figure out which controller you like more. then figure out if bluray is something you want and THEN think about if you want to pay to play online. once you answer those questions you will be able to pick a system for you.