Just to add my nugget of wisdom(?). I am the proud father of a 3 year old and a 5 month old. My 3 year old is very bright (she is almost reading now) and has shown a keen interest in what I do on the computer. So far, she just hangs over my shoulder and watches me code, she knows that I write "perl code", but she does not grasp the concept quite yet.

However, she truly enjoys chess, my wife and I both play, and we introduced Eden to it about a year ago. Start off real slow, just show her how to move the pieces, and let her win a lot. She is obviously still not a challenge, but she does get a kick out of it, and she is learning more as time goes on.

Good luck, best wishes, and as someone else said here earlier, spend as much time as you can with them early on, it moves SO incredibly quick

As I think anyone with a child about this age could tell you:
The handprints on the wall get higher and higher, and before you know it, they are gone.
Source unknown.