I've read several reports recently of bloggers whose three-year-olds love board games. The grandma-santas were kind enough to supply us with a few kid-appropriate games, so we've been trying them out. The kids think they're fabulous!*
*I should also add, for full disclosure, that coaching them through a game of Candy Land is a bit of an athletic event. I was envisioning quiet family time where we all sat around the table and moved our own pieces around the board in an orderly fashion. Currently it involves lots of reminders not to eat the cards, not to sit on the board, not to eat the pieces, that you can't switch pieces mid-game, you can't jump your piece ahead forty spaces just because that part of the board is prettier, etc.