Open Transport Tycoon Deluxe:
http://www.openttd.org/en/
It's free, it's addictive, and can be customised with additional grfs, you want to play with British trains from 1900 to 2000, there's a grf for that, Dutch trains, yup, Yank trains, they've got it covered. All through an easy to use downloader which interfaces with the games GUI.
FreeCiv:
http://freeciv.wikia.com/wiki/Download
FreeCiv is based upon the popular Civilization series, it may not be as pretty as modern Civ games, the graphics level looks to be around the Civ II/Test of Time/Call to Power II level, but it's free and it's Civ-like. Does more need to be said?
FreeCol:
http://www.freecol.org/
I've never played Sid Meiers Colonization, I've never played FreeCol, but it's a Sid Meiers game, so it's probably going to be good.
Warzone 2100:
http://www.wz2100.net/
A nice little game this, RTS with the ability to design and build your own units. The AI isn't too shabby, and the graphics are quite nice.
And much much more:
http://en.wikipedia.org/wiki/List_of_open_source_games
http://en.wikipedia.org/wiki/List_of_freeware_games