Most all of the more difficult games I have beaten were back in my childhood on NES.
Double Dragon 1-3
Ninja Gaiden 1 and 2
I feel like I beat Battletoads at one point, but I might've just watched my brother do it. He is much better than I am at pretty much all video games.
Someone mentioned Vagrant Story, not sure I would classified that one as difficult but if so, throw it on my list here too.
My brother and I used to double team games, too. Some he was great at (Metal Gear, Ninja Gaiden, sports games) and some I was great at a few, too (Castlevania, Bionic Commando, Wizards and Warriors, space shooters). We'd "give each other credit" by totally beating a game, getting to the final boss, and letting the other get the final hit.
Good memories. Now, he doesn't even game anymore. He's a preacher. Such a waste!
Just kidding. He does good work.