Wow, so many good games...where to start?
For more recent stuff:
Gunstar Super Heroes -- kind of easy on Normal mode, but on Hard it's amazing.
Astro Boy: Omega Factor -- all around excellent game
Metroid Fusion/Metroid Zero Mission -- both of these are great, although I personally like Fusion better.
Gradius Galaxies -- I've sunk many, many hours into this shooter.
Sigma Star Saga -- just finishing this game up...I personally think it's great, although the first part of the game is kind of tedious.
Many more great games...I haven't got time to go through all of them.