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I'm not necessarily referring to perfectly historically accurate games. Any games with attention to period authenticity will do. I will update this post as new games are mentioned.

Games mentioned so far:
Age of Empires
Codename Panzers
Field of Glory 2
Hearts of Iron 3
History Line: 1914-1918
Kingdom Come Deliverance
Mount And Blade
Panzer General
Post edited July 20, 2019 by RedFireGaming
I've enjoyed Mount and Blade quite a bit since it first came out and online can be somewhat fun.
Two strategy games that may help to enlighten some dynamics that have happened in history.

Civlization: all the series is good, but the best of the most recent is Civilization IV. This game has actually been used by history teachers. If you get Civ IV, set the graphics options to the max and you will find it looks really good. There is a mod that improves the game experience. Check the Civilization forum in GOG.

Imperialism: Focused in the stages of capitalism that lead to imperialism. An amazing game. There is a sequel that starts in the Age of Discoveries, while the first one starts in the napoleonic age and runs up to the Great War age. The 2D interface is serviceable and we might say close to ageless.
1Zpn7QM3: I've enjoyed Mount and Blade quite a bit since it first came out and online can be somewhat fun.
Good game. Still unsurpassed handling of horses and mounted combat. Not even AAA titles have managed anything like that. I will say it again: Horses!

Dunno if it can be called historical, though!
Post edited July 19, 2019 by Carradice
Kingdom Come Deliverance, love it.
Field of Glory 2
Hearts of Iron 3

I would like to say Crusader Kings 2 but it's too fantasyish for me.
Post edited July 19, 2019 by ChrisGamer300
History Line: 1914-1918
Codename: Panzers 1 & 2
Panzer General series
Civilization series

Modern Age
Balance of Power: Play as the US managing its international relations in the Cold War
Hidden Agenda: post-dictatorship scenario in Latin America in the 80s
Panzer General series: Especially interesting about scenarios taking place further away (for me as German the Pacific scenarios)

Does JFK Reloaded count?
Medal of Honor.

Specifically for the fact that it is the only WWII FPS that I know of that includes missions based around Operation Torch in 1942.
Expeditions: Conquistador is pretty nice, makes good use of the setting and gives you quite a bit of choice (you can play as humane explorer, as genocidal imperialist or as something in between).
Age of Empires 2 was also really fun.
I liked Sniper Elite V2 and 4 (haven't tried the first or third).
Darklands. An RPG set in the medieval Holy Roman Empire. The game and manual teach you about things like church life and popular saints of the time while you fight highwaymen and creatures drawn from folklore.
Definitely Stronghold and Crusader (stand-alone expansion)
Is this strictly limited to GOG only? If not, Total War games definitely should be mentioned, except Total War: Warhammer.
My favourites are:

1. Rome Total War (the first game of the name)
2. CivCity Rome (as the name implies, a city builder taking place in Roman times)
3. Battlefield 1942 (though you'd need the Forgotten Hope mod to play with historical accuracy)
4. Age of Empires II (because you can play as historical figures from the middle ages)
5. History Channel Civil War (a first person shooter where you play both as a Unionist or Confederationist
soldier in the US Civil War, though it only runs under Windows XP for me, I finished the game on my retro rig)
6. Children of the Nile (a city builder that lets you build pyramids as well)
7. Age of Empires (the first game in the series was the first PC game I played)
Post edited July 20, 2019 by DubConqueror
Children of the Nile
Emperor: Rise of the Middle Kingdom