I couple people I know mentioned buying a Wii for Christmas for their kids.  I thought I'd compile a list of some of the games my kids have and/or have rented, along with my feedback (from me observing them).

By the way, I have a 10 yr old girl, a 7 yr old boy and a 5 yr old boy.

1. MarioKart Wii -- Kids really enjoyed it, particularly my 5 yr old.  Can even easily race other drivers over the internet (Nintendo makes it so they can't chat, but the game does show what country they are connecting from).
2. Lego Indiana Jones -- Kids really liked it, particularly my 5 yr old.  Basically walks them through all 3 Indiana Jones movies.
3. Lego Batman -- same as Indiana Jones (but with Batman).
4. Lego Star Wars -- you guessed it...same as Indiana Jones (but with the 6 Star Wars movies).
5. Super Smash Brothers Brawl -- one of the games my kids about wore out.  Your standard cartoon characters "battling" one another.
6. Go Diego Go Safari Rescue -- my 5 yr old had a lot of fun with it, but it quickly lost its charm.
7. Boom Blox -- One of the best Wii games Ever. Good thinking/strategy game to play with your kids.  http://en.wikipedia.org/wiki/Boom_Blox
8. Star Wars Force Unleashed -- Star Wars.  Kids.  One of the only games I've ever seen them play through the end of the single player game.
9. Wario Ware Smooth Moves -- Older game (hard to find, may need to buy used).  Humor can be a bit juvenille (fyi if you insulate your kids from that).  Great party game for kids and/or adults.
10. Rayman Raving Rabbids -- Another good game with a mix of playing modes, from shooting toilet plungers at rabbits to moving the wiimotes up and down frantically to make a character run.
11. Boogie (Karaoke) -- One of our less intelligent purchases (which is only to be played with mom and dad in the room (Dad isn't too keen on his daughter (or boys) singing "My Humps" (etc)).

Always rent before you buy (if at all possible).  There are some Wii games that require so much skill/timing that a young kid would be VERY frustrated.

There are a number of websites that provide game reviews (to help you weed out those with "potty humor," etc. (if that is important to you)). 

The game review sites also grade the games.  If a game is a 9/10...it probably isn't a dud.  Here's a link to one such site:  http://is.gd/9OCP.>

The Nintendo Game Cube games work on the Wii.  That greatly opens up your choices when it comes to games (particuarly cheap games).  My daughter is a HUGE fan of the Animal Crossing games (sort of like the Sims for kids).

You can download hundreds of old Nintendo games (for $5-$15 each) via the Wii's "Virtual Console."  You can also buy/download new games written by third parties via "Virtual Console."  That is how we picked up one of my daughter's favorite games of all time, the puzzle game "World of Goo."  http://en.wikipedia.org/wiki/World_Of_Goo

We bought a Wii Fit some time ago...my kids never did use it much.  Perhaps we need a snowboarding game...

Hope that helps get you all started.