Learn to play
Go.
It's fun, and you'll never stop learning until you stop playing (the highest level professionals guess that a bit over 10% of the total game theory has been developed).
The game is at least 4000 years old (archaeologists have found what look like go boards older than that, but they guess they were originally used as some sort of fortunetelling device).
It is a total information game (no randomness, no hidden cards or other variables) yet the strategy is so deep that computers suck at it.
I can get an even game with a computer, and my roommate can give a computer a 9 stone handicap (9 moves on the board before he plays his first one) and win easily. One time so far in history a supercomputer beat a professional player. The computer had a nine stone handicap and only won by 1.5 points. The supercomputer was approximately 1000 times the power of Deep Blue (the computer that beat Gary Kasparov at chess). That was last year. There have been two attempts at supercomputers defeating pros with smaller handicaps this year (8 stone and 7 stone) - both resulted in overwhelming victories for the pros.
Also, at the time Kasparov played Deep Blue he was probably the world's best chess player. The pros who are playing the supercomputers at Go so far are not even in the top 100.
Rule tutorial and some tactics/strategy lessons:
http://playgo.to/interactive/The best go server (in my opinion); friendly atmosphere, lots of lessons available, easy to find a game:
http://www.gokgs.comSomebody else I directed there from this forum here said that his computer locked up when he clicked "Play Go Now" - I guess his Java plugin was out of date. Just in case, use the "Download client and SGF viewer" link instead - it'll give you a handy desktop icon anyway.