Board games for little kids and their parents

My daughter, Poesy, is coming up on four years old and she's starting to enjoy rolling dice and counting the pips, so we figured it was time to start thinking about board games. My wife, being the games professional in the family, asked on Twitter for recommendations and did a monster roundup of what all the game-type people in her social circle recommend. I'm dubious about some of these choices (if my kid falls in love with Monopoly or Candyland or Snakes and Ladders and demands that I play them with her at great length, there will be trouble), but others look like good fun for grownups and little people. We recently went for a weekend away with a bunch of friends from the games industry and were overawed by the sheer volume of killer board-games that filled the rental house. I'm really looking forward to Poesy being old enough to play Elefanten Parade, and (especially) Waldschattenspiel, an absolutely beautiful and extremely fun game for one adult and two or more kids.

Do you have a board game that your little kids love to play and that you find enjoyable too?

Boardgames for kids: roundup