I spent a few years of my life playing:
Heroes of Might and Magic 2 PC - I had never played anything like this before back in the day. When i first played it at my friend's house, I couldn't stop. My friend's mom came downstairs and yelled at me to leave! I saved up all my money for a few months and bought my first computer just to play this game. This was a long time ago. The recent Heroes 5 game is pretty good but I never got obsessed with it like with the second game of the series.
Disgaea PS2 - This has to be THE strategy RPG of all time. I must have logged hundreds of hours playing through this. I guess I became addicted because there's so much to do in the game. You can focus on leveling up a character, unlocking new characters, leveling up items, or just about a billion other things. I later bought a PS3 just to play Disgaea 3 but I was kinda dissappointed by it. The original is the best.
Civilization IV PC - I can't stop playing Civ4. Well actually I haven't played in a few weeks but I absolutely love this game. With the Beyond the Sword expansion, the game is complete. I'm currently playing at Emperor level. Greatest strategy game of all time.