While this one might not count, since Mario's Time Machine is barely a 'game,' it is the rare Mario-meets-the-founding-fathers crossover that the fanfic community desperately needs more of. In it, you are sent back to 1776, the founding of America and the signing of the Declaration of Independence. For some reason, the Declaration has been lost, and you have to find it and return it to the founding fathers. It's a good thing Mario didn't use his time machine to go to Philadelphia in the present day; it would have been a much different, much more violent game.
I don't know what it is about colonial America that makes it such an enticing place for a game to be set, but we learn through this classic time-travel adventure game that the Constitution was actually created on the same site as the Maniac Mansion. A cool thing about this game is that many characters from this level can be seen later in the game, in different time periods. For example, Betsy Ross is later shown to be Ed Hardy.
If you successfully complete the single-player mode of Black Ops, you get a bit of fan-service called "zombie mode." While killing zombies would be enough of a treat, this mode offers so much more, as players assume the roles of Richard Nixon, Robert McNamara, JFK, and Fidel Castro in a secret meeting that gets interrupted by bloodthirsty zombies. If the Nixon-Kennedy debates had been like this, history class would be a lot more interesting.
Abraham Lincoln's exaggerated features make him a comedic staple, so it makes sense that he would appear in the slapstick world of Sam and Max. Chapter 4 of their episodic adventure game is titled "Abe Lincoln Must Die," and features Max running in an election against a giant statue of Abraham Lincoln, a statue the pair must eventually blow up with a bomb. Assassinating a giant statue of Lincoln? Too soon, Sam and Max. Too soon.