Image: Civilization 3
It's not the best of the modern Civilization games, but it's a perfectly playable game with expansions. And, more importantly, it's free.
The complete Civilization 3 bundle is free for the next day and a half over at Humble Bundle. It's traditionally not an expensive game anyway - $US5 at full price - but free is better than not free, and a free Civ game is a hell of a lot more replayable than plenty of other games on your Steam library.
Nonetheless, it's a good place to start if you've never tried a Civ game. Once you've got your feet wet, here's a Middle-earth total conversion. There's another one that transforms the game into Heroes of Might and Magic. And if you like Warhammer, there's a mod for that too.