My husband's a huge game geek, and has a small collection of games specifically for playing with our nieces and nephews and friends' kids (and hopefully someday our own kid). Two that have been really successful: Gulo Gulo (sort of Jenga-like, but little kids have the advantage because the pieces you need to remove are really small) and Reiner Knizia's Flea Circus (a card game with no reading involved, and you keep score with plastic cats and dogs, which my nieces love). Also, boardgamegeek.com has ratings of hundreds (thousands?) of board and card games, including info on which ones are good for different age ranges.

Orchard. No loser...KEY!

Orchard is a wonderful kids game, we got it when my son was 3 and it is a wonderful introduction to games. I went for orchard rather than my first orchard and while It can be a pain to find the little fruit at the end of play I'm glad I went for the full version

I posted a post on our favourite family games recently... including heaps of card games and games for little people. Probably our favourite family game is Cadoo... but there are heaps of games by Beleduc that are brilliant for very young players. Here's the link to our game post: http://www.se7en.org.za/2012/12/15/se7en-1-s-favourite-games-family-games-classic-games-and-card-games

Take the Cake and Snail's Pace Race are awesome. The Yoga Garden Game is also popular, as well as matching games... eeboo has a cute one.