Heck, if it was paper and pencil RPGing you wanted, there’d be no reason not to use D&D - just run an absolutely magic-free campaign with no fantastic creatures. There wouldn’t be much point playing anything but a fighter, a thief or maybe a modified bard (monks just have too many fantastic elements built into them). Or if you wanted a more realistic simulation, try the RuneQuest system with no magic, and be prepared for your first fight to end in maiming 'cos those location-based combat systems generally end in the loss of an extremity or a killing body blow if you don’t have magical healing to hand.
Not an RPG, but maybe still of interest to you: Crusader Kings by Paradox Interactive. You play a feudal lord over a domain in medieval Europe. It’s a mostly strategy game, but characters do have personal attributes. You can play it to strictly optimize your realm, but I had fun role-playing it instead. You have courtiers and relatives and heirs to deal with, plus your neighbors, liege, and vassals to interactive with. It should be pretty cheap to buy now.
As for a more traditional RPG, you might look into mods to Oblivion. That game is highly customizable. It quite possible someone has developed a no-magic mod.
You guys just made me laugh out loud. A lot. 
Assasins Creed is Fun, I’ll give you(particulary the stabbing, but also the running(and more stabbing)) but it’s not terribly historical accurate. That and it pretty much relies on the concept of a genetic memory interpretation machine to pull off.
And then there’s the “Pieces of Eden”. Yeah. Just those…
Or GURPS where medieval characters don’t have those kinds of survival troubles.
Or Pendragon where you can say Merlin is just a wise man who knows a few parlor tricks and run the system straight.
Or one of about two dozen non-magic medieval period RPG’s that function just fine without some kind of magic user to hand out healing every few minutes or an automatically evil species that the players can feel good about killing.
I played Assbandit’s Creed, for all of ten minutes. It sucked. The high-tech virtual-reality-simulation aspect of it was SO FUCKING STUPID; why couldn’t they have just set the damn game in the historical period and left it at that? The dusty, dull gray-brown color palette was about as interesting to look at as a camel’s ass; I realize it was that way because it was set in Jerusalem or something…well guess what, that was a shitty setting to set it in then. I want to see some red, blue, green, yellow and purple and stuff every now and then. (At least Medieval II Total War is extremely colorful, although it’s not the kind of game I’m talking about.)
I just want a game where I can play as a badass knight in badass armor, riding around on a giant horse, and hacking people to death with swords and maces. And the ability to upgrade and customize armor, and earn skill points, and meet other heroes and form parties and develop alliances. What is so impossible about that kind of game?
Lack of imagination on too many people’s part would be my guess.
I was going to joke:
The Original SimCity
Because:
What?, It looks Medieval by today’s standards. :eek:
But then I remembered:
Oh wait, you can have your City smashd by Godzilla in that game. Nevermind.
So it still fails the OP. 
My opinion: because unless the developers were able to introduce enough variety and unique concepts into the game in order to make up for the loss of the many gameplay elements that must be discarded by appealing to realism rather than fantasy, that kind of game would not be fun.
I actually thought of another one. It’s a shareware game using the Rogue engine set in medieval Finland, alled Unreal World.
http://www.jmp.fi/~smaarane/urw.html
It doesn’t have much of a plot, though.
Your opponents are all the same?
If you insist on realism, it’s hard to see how yourself or a small party would have a medieval story.