strategy games
Age of Empires was the game that got me hooked on strategy games. Civilisation was the game that made me need to seek a self-help group 
Both of these games are bring out new versions soon.
Civ 4 (right)
The development team are apparantly working hard on simplifying the user interface, adding new features and ensuring that the traditional playability is still there. One article that I read talked about how they are putting some effort into making the turns take less time when you get further advanced in the big games. That is good news as in Civ3 this can detract from the enjoyment levels quite a bit.
Age of Empires (left). The new version shows an amazing video engine. I just hope that for both Civ4 and Age of Empires 3 we don’t see a downgrading of playability for the visual benefit.