Battle for Wesnoth is a great recommendation. It's pretty simple to understand the rules, you can set the difficulty to suit you, it's fun, and it's free (plus i really like the music).
Europa Universalis is pretty damn complex and clunky. If you want something streamlined and easy to get into, that is definitely not it. Or anything else Paradox Interactive makes.
Frozen Synapse is a cool looking indie turn based strategy game I've had my eye on.
HOMM 3 is not too complex (especially compared to Civ), and is a lot of fun.
Alpha Centauri is my favorite "civ game" because of the cool setting, story, and ability to create your own custom military units, but it is a little complex, especially the terraforming which I still don't really understand. It's also like $6 on Gog.
Simcity 4 is fun and it's sorta kinda a strategy game.
Europa Universalis is pretty damn complex and clunky. If you want something streamlined and easy to get into, that is definitely not it. Or anything else Paradox Interactive makes.
Frozen Synapse is a cool looking indie turn based strategy game I've had my eye on.
HOMM 3 is not too complex (especially compared to Civ), and is a lot of fun.
Alpha Centauri is my favorite "civ game" because of the cool setting, story, and ability to create your own custom military units, but it is a little complex, especially the terraforming which I still don't really understand. It's also like $6 on Gog.
Simcity 4 is fun and it's sorta kinda a strategy game.