Going way, way back, there’s Master of Magic, but it’ll take some work to get it running on a modern PC. Fantastic game, though.
Also old, but easier to get running, is the Five Star General series. It includes Panzer General, Allied General, Pacific General, and Panzer General II, which were all set in WWII, plus Fantasy General, which uses the same mechanics in a fantasy setting, People’s General, which is a near-future war between China and some of its satellites, and the US and Russia, and Star General, a sci-fi version set in David Drake and Bill Fawcett’s The Fleet universe.
Agreed. The balance is better. The AI is better. The AI will kick your ass into next Wednesday. The races are cool. Oh, and if you look at it funny-like, the AI will FUCK YOU UP. Did I mention that, already ?
The original was great as well, and for a while was available as freeware.
I never played the 3rd. I heard horror stories about it.
I thought about mentiong the MOO series, but it doesn’t have the “icons travelling around the map” thing that the OP mentioned, so I wasn’t sure if it’d be what he’s looking for.
If he wants a more modern version of Space-set turn-based strategy, Galactic Civilizations II is a great choice.
To put in a fairly shameless plug for my favorite entry in the space strategy genre, Sword of the Starsis everything a sequel to the ORIGINAL Master of Orion should be. High points include:
Races that are sincerely different in meaningful ways
Abstracted colony management to give you time to focus on the interesting bits instead of “Now I build a hydroponic farm on Zeta Reticuli”.
Huge arsed tech tree with semirandomized techs (The tech tree is the same every game, but which techs you will actually have -access- to varies by game and race.)
Straightforward interface design
The SOTS demo sucked me in in an eyeblink, while Galciv 2 had me flailing around wondering what the point was. YMMV.
I hear nothing but good about the Civ4 Mod “Fall From Heaven 2” which apparently repurposes the game to a Fantasy setting. That said, that’s a second hand recommendation since I don’t even own Civ4.
My issue with H4 is almost wholly with the AI (as I think I’ve said here before). They basically revamped just about everything (H5 is much more of a throwback), and, while some things needed balancing, I did find the skill system to be very satisfying. But the AI on the adventure map was hopeless; the only really playable scenario was one which was rather linear and scripted-as in being more of a RPG experience than a strategic one, but I usually prefer the latter to the former. The mod for H4, Equilibris, has only been marginally successful in remedying this.