Over on t'Whoblog, I mentioned the old World Of Darkness portrayals of Rasputin in the context of Celebrity Historical episodes. On the whole, these tend to "print the legend" as in Westerns, as Mark Gatiss put it when talking about his depiction of Churchill.
So how to portray real people in other games?
An urban fantasy or horror game like World Of Darkness might focus on the strange mysteries of history, where someone like Rasputin seems fair game, but the third-party Call Of Cthulhu adventure "Secrets Of The Kremlin" which had Stalin actively studying the Mythos seemed a bit tacky. (To say nothing of one of those Rasputin appearances being in the same book as vampire Himmler, since quietly ignored.)
Of course, this is the real(ish) world, and care must be taken to cause offence in some cases.
Teaming up with the President in a superhero game? Or possibly Prince William, ace helicopter pilot? Heroic portrayals can be pretty amusing. Conversely, use of real "villains" makes me twitch with discomfort.
Beyond our history, some fictional settings have detailed enough backgrounds that you might have stories of modern, historical and legendary figures ready to go. "So who's this Conan guy anyway?" You could add characters the PCs would know about, but it's more involving if the players recognise them as well.
I can imagine historians in fantasy worlds arguing about portrayals of ancient heroes. That "Know, O Prince..." opening has always made me wonder who's talking, and to whom.
And if the PCs are ever flung forward in time, they'll probably be rather surprised by how history remembers them. "We gotta go to the crappy town where I'm a hero!"