Nothing competes with Europa Barbarorum as far as historical accuracy. (I've never managed to get it to work on my computer, but I read rave reviews wistfully.) These are incredibly in-depth mods to the Total War series, made by a team of scholars. Buy Rome: Total War, then download Europa Barbarorum I; or buy Medieval II Total War, then download Europa Barbarorum II.
I'll quote from their (Rome) site to give you an idea:
Faction specific naming practices with accurate unit names and accurate province names in the language of the controlling peoples at the game's start.
Accurate terrain reconstructions, snow boundaries, vegetation types, and coastlines.
A complex new government system has been introduced to more accurately reflect the choices of government types available within individual factions for the provinces they begin with and conquer.
New Classical Latin, Greek and Celtic battle map voice recordings, thoroughly researched and complete with accurate ancient pronunciations and accents.
On some topics, this video game might actually be the best learning material available outside of academia. It's insane.
I also recommend GeopLP's video playthrough of Assassin's Creed 1 & 2 here. He's a geologist, so don't take it as authoritative unless he's talking about marble varieties, but he puts a lot of effort into his research and presentation, even interrupting the Let's Play for educational slideshows sometimes. And architecture lectures get way more fun when you're watching someone ninja climb up the building's surface.
If you like sprawling RPGs with 90s-era graphics, Nethergate might be your thing. It's a fantasy story, but set in Roman-occupied Britain. I haven't got too far into it yet, but my impression is that history is a light flavoring. Someone will tell me which Celtic tribe is rebelling, or mention how Celts made shoes, but most of the time I'm killing goblins. It's fun, but if history is your main goal I'd put this one a distant third.
Although fictionalised, the 'Metal Gear' storyline on international relations during the cold war era is one I would recommend most. There's a lot of in-depth information on the individual agency of some well known historical figures.
I started off with Metal Gear Solid 3: Operation Snake Eater. The game teaches its players, if you're prepared to sit through an amount of cut-scenes lasting at least as long as the entire game, a lot on the scope of the international situation (whichever that may be).
I would recommend Victoria 2, because although it does have many inaccuracies, it depicts well the struggles experienced by leaders in the time.