@zhjuan,
Learning is about having fun, which is why games are effective. Of course, different people find different things to be fun which makes answering these types of questions so difficult.
Why not let your child choose something that interests her?
My older sons really liked strategy games-- we played some turn based computer games that gave us the chance to figure out and discuss strategy. One of my sons really liked the funny little card/dice games you can buy at book stores in the US that involve cows and space aliens and strange rules about transmorgification).
Then there are the classics. I taught my kids poker (which every kid should know how to play) and chess.
My daughter is 5 years old... and the ability to cheat (i.e. hide the ice cream cone card in candy land) was a innovation that impressed me (she had the sophistication to understand what card she needed to get to win the game, and the creativity to figure out how to ensure she got it).
But, it is the time you spend interacting with kids that is more important than the specific activity.