Kid Icarus definitely has to be up there. I rented it as a kid and couldn't figure out how to get past the beginning. Are we talking games we've played or games we've beaten? If it's played, then it's pretty much gonna be a bunch of NES games for me. If it's beaten, then it's probably not all that hard. One game that stands out (though I'm not certain it's the hardest I've ever beaten) is Brave Fencer Musashi, which mostly isn't that hard, but I found the button mashing on the second form of the final boss difficult. Combine that with the fact that if you die you have to go through a whole bunch of stuff again including another boss before the final boss, story sequences, two platforming sequences of getting chased by the final boss before fighting it, and the first form of the final boss, and it was incredibly frustrating. Ended up putting it down for years before finally completing that game.
Anyway, that's one for toughest played and one for toughest beaten. That's all, because it's hard enough to come up with one.