As bookends to a line on the OP list, there is Caesar 3, and Children of the Nile.
Also, freeciv. It's a FOSS recreation of the best of Civ1/Civ2 DNA, and has been at it a while, so the game should be stable and robust.
Finally, Grand Ages: Rome. It's a Roman historical city builder from the folks that did Tropico.
Caesar 3 I could never get into; I started playing with Pharoah and it felt like a huge step back, missing a bunch of the goodies that made it decent. All of those city builder games minus Rise of the Middle Kingdom came in a multipack that I had gotten ages ago. Zeus/Poseidon and RotMK end up being the most playable for me these days, while Pharoah/Cleopatra are a labor of love, in that I absolutely adore the setting, it's like Caesar to Pharoah, and is missing a bit that the later games made less frustrating.
FreeCiv is somewhat difficult to go back to after playing the later versions of Civ3+, but it does have an Android version, so that's a plus.
The Fall From Heaven 2 mod for Civ 4 was great, and the different factions had a good bit of flavor to them.
FreeOrion I had not heard about yet, but it has been downloaded.
Gratuitous Space Battles having a campaign mode would make the game a bit more interesting; as it was, just doing one shot skirmishes with various combinations of tech got fairly old quickly.
Updated the main post with those games I had forgotten I played (Crusader Kings 2, Call to Power 1/2, SimEarth, Master of Magic, Civ4 FFH2, MOO2)
Also updated the post with games I haven't heard of/tried before (Grand Ages: Rome, Cultures 1/2, Victoria 2, Enemy Nations, Pandora: First Contact)