Cave Story in itself isn't that hard, but the secret final level (to get the good ending) is ridiculously hard. I've gotten to the final boss but I still haven't beaten him yet. The boss himself might not be the most difficult thing in the world, but the entire level is a gauntlet, complete with another boss you have to fight before the final boss. No checkpoints, and if you're lucky you still have the 1 Life Jar the game gives you.
Also, music rhythm games like Beatmania and DJMAX can have some very difficult note charts for songs. There are songs like
Nightmare and
Angelic Layer. There are DJMAX games for PSP as well as the pc DJ MAX Trilogy. Beatmania is an arcade game, though you could find ways to play on your pc. Beatmania I have to warn is extremely strict with timing, and is for masochists only.