I've beat Contra, Super Contra, Contra III, Contra: Shattered Soldier, Contra 4, Mega Man 4, Super Punch-Out!! (the last 2 fights are ridiculous), Devil May Cry 3 (black label US version on the most difficult setting), U.N. Squadron and Ninja Gaiden III without any cheating, codes, etc. Which one was the most difficult? I don't know...probably either Contra: Shattered Soldier or Contra III.
I actually beat Shattered Soldier the first night that I had it. I played with a friend for a few hours and, after he got too frustrated, beat it by myself while he watched only dying once. The last thing I remember him saying that night was "How the FUCK did you just do that?"
I think the key is memorization on all of these games (other than DMC3). If you can memorize each level then you're good to go. I managed to beat Ninja Gaiden III last week after playing it for about 4 hours or so. I can fly through the first 5 levels without dying now (usually) and it's all because I know exactly what's coming at me. Basically, when I play a really hard game I just turn into a robot until I get to a new area. Once you have it down you can beat any of them without a problem. I can still sit down and beat Super Contra in one play through if I go into robot mode because I spent so much time playing it as a kid. Probably the same reason I can sing the theme songs from Ducktales, Darkwing Duck, Ninja Turtles, etc after years and years of not hearing them