Sid Meier's Civilization II (PC Games, 1996)

Simply my favorite game. Most games are either easy to begin playing but lacking depth, or very challenging but very difficult to begin playing at an acceptable level. Civ is the odd exception, It is very simple to begin (an easy level with a good tutorial), and can get very difficult, while constantly revealing new subtleties in gameplay. The ways you can play it also allow you to tailor the game to your personality - world domination vc. diplomacy vs. space exploration. The same is true of the technologies you can build - armies, libraries, banks, etc.

I have played, and continue to play the later versions, which have signigicantly better graphics, but this is still a great game. One plus is that the entire game can be loaded onto your hard disk, so you don't need the CD in a drive to tun it. My wife has tried each later version, and always gone back to Civ II. There are also a number of add-on packs to increase the versatility further - you can re-fight World War II or an alien invasion.