Civilization - the first refined 4X game. Manual the size of a book, plenty of strategies and just enough random chance to make each game exciting. I played the series till the fourth one, and I'm still spending too much time with Civ I and IV. I also branched out to Master of Orion, Colonization, Alpha Centauri and others.
Dungeon Master - A wonderful and challenging dungeon crawler, which convinced me that the best RPG mechanic is party-based first person. This was my launching pad for numerous games and series, in particular Wizardry, Might and Magic, Eye of the Beholder, Lands of Lore, the Ishar Trilogy and Realms of Arkania.
Warlords - 80 castles, 8 factions, lots of unit types, magic items and a complex way to fine-tune the difficulty level makes this endlessly replayable. This game launched its own turn-based fantasy strategy series, but it also introduced me to other series I still play, such as Heroes of Might and Magic, Age of Wonders and Disciples.

Honourable mentions:

UFO: Enemy Unknown - turn-based tactical combat with a good mix of budgeting, manufacturing and research. I also appreciate other series, like Incubation and Jagged Aliance, but I'm always returning to UFO and its successors for the economic simulation.
Panzer Commander - This game dumbed down historical strategies for me, to the point where I would actually enjoy it. The whole series is brilliant, and I still occasionally replay it.