I see a lot of people suggesting wars and major conflicts (though thankfully, some suggestions of crime, like Ned Kelly, and colonization, like the fur-trappers in Canada.) I think people get too caught up in that. While conflict is a good basis for a game, it does not have to be in the setting of war, and more importantly, not having a clear good and evil side opens up explorations of humanity (especially when you get to choose the side you want.)
Well, lets think for example, a time period not often explored, and a job not considered. Seeker of the Dead in the era of the Black Death in Europe. Your job is basically an early epidemiologist... or to put it in laymans terms, you look at lots of dead people and where they were and how they died to determine how a disease is spreading, and find ways to stop it to save your town, country, whatever. You would go to houses on a map, find the corpse, determine how it died, and add that to a large chart and decide to leave them be, quarantine the house, burn it, kill everyone inside, quarantine the town, etc. Higher up, you could make suggestions to burn the bodies, bury them, leave them to rot and forbid anyone from going near them, kill certain animals in the area, burn everything and move the survivors to a different town, forbid anyone from leaving the town, all for the good of protecting whoever you are loyal to, be it the lords, the people, the land, the country, the king, or yourself. Although, in this example, it is still somewhat cut and dry... you are good, the plague is bad.
Honestly, to get games that move away from that, you either have to have neutral sides on a conflict, a third party in the middle of a conflict, or no conflict (kind of like Kerbal Space Program.) For neutral sides, I would love to see anything involving the Indian Sub-continent pre-colonization, Dark-Ages Europe, or Russia pre-Napoleon (really, any time before that.) For third-party, just give a random person a pivotal role in some conflict anywhere in history where tipping the balance either way could be a clear victory for one non-completely-evil side or the other (personal favorites being the split of the Roman Empire, the wars in Carthage, anything in the Middle East, any native group negotiating between several colonial powers in Asia, Africa, or the Americas, any part of the Hundred Years' war, or the Ottoman Empire.) For no conflict, I am partial to the idea of an epidemic game, set in say, the 1800s, where names are barely known, symptom reports are all you have to go on, treatments are rudimentary, and you really have to guess to find causes that can range from diets to parasites, from airborne to waterborne, from human intervention to human waste; in such a game, all you would have to go on would be your knowledge going in, the information you have, logic, and trial and error to solve such a puzzle.