I play my Wii every weekend I'm home, although I'm inclined to believe my Xbox 360 gets more play hours. The DS is with me at school, so it probably gets more hours then either console.
I don't know why the Wii doesn't get so much play time. I think there's many good games, although my 360 library is almost twice the size of my Wii library.
I do also play a lot of Virtual Console games. The memory is full. I have about two pages full of games. I copy the save of games I completed to my SD card and download a new batch of games that I want. It helps I missed out on much of the N64 generation and to a certain extent the Genesis generation (did not get much love when I was younger). My Wii is also the only way I play my GameCube games, and I've got plenty of backlog for that console, too, and I'm still adding games to my GameCube library.
As far as actual Wii games go, I've beaten a lot of games, just not to 100% completion. Zelda I beat in like 20 hours during last Christmas, but don't have all of the hearts and bugs. Wario Ware could use a few more mini games unlocked. Excite Truck I unlocked Super Excite Mode and stopped. Super Mario Galaxy, I was at like 90 stars. I don't have all of the extras unlocked in Battalion Wars. In Super Mario Strikers Charged I'm missing Petey and some of the cheats. Super Paper Mario has logged a good 25-30 hours, but I lack cards and apparently some optional Pixls (checking GameFAQs). Oh yeah, and I finally finished Link's Crossbow Training (mostly bronze and silver medals). Dewy's Adventure, Elebits, Metroid Prime, and Zack & Wiki are my only remaining unbeaten Wii games.
The other issue with the Wii is ports. Not only is the quality usually worse, most of them, it's just better getting the Xbox or PS3 version (depending on your console). I'd probably have a larger library of games if 3rd party games were actually worth getting. I have heard good things about Prince of Persia, The Godfather, Scarface, etc., but so far, at best, they've been only rental-worthy or I'm having trouble with the thought of paying $50 (or $30 in the older games) again when I could play the superior Xbox/PS3 version. It's unfortunate, but I don't think the Wii remote is enough to make me pick a Wii version of a game. It seems like graphics and other features are beating gameplay. Granted I still have a list of games I want such as No More Heroes, Resident Evil 4, Geometry Wars, etc.