Oh, this is actually a bit of an old topic, but why not.
I don't really seek out hard games, but a couple stand out to me:
(1) F-Zero GX. It's an amazing and incredibly deep racing game. It has a fairly steep learning curve, and the story mode is infamous for its difficulty (Chapter 7, anyone?) - even when it gets frustrating, though, the graphics, music, and adrenaline just keep me going.
Even after clearing story mode and beating the time attack staff ghosts, there's a ridiculous amount of depth left in this game if you continue to work on your times. I'm just barely in the top 50 of the
max speed rankings. I pretty much know what the leaders are doing, but the top strategies for pretty much every track are absolutely insane, as the large time gaps in some of the rankings will attest to.
One of the more notable techniques is an
edge boost. If you drive your car off the edge of the track and then immediately drive back on, you can get quite a large boost of speed. This can save obscene amounts of time in some stages, but every time you attempt an edge boost, you're obviously risking falling off the track and ending your run.
(2) Shoot the Bullet (Touhou 9.5). The Touhou series in general is really hard for me since I'm not good at shmups, but Shoot the Bullet kept me going a decent bit longer than the other Touhou games. The stage-by-stage format is pretty addicting, and there's not too much pressure while playing because the stages are so short. Again, though, it is very difficult for a non-shmup person like me. Some of the scenes took me hours to finally clear (and others, hours to
not clear), though I managed to unlock Extra after keeping at it for a while, and I'm pretty happy about that.