Here are
some of my suggestions, talking by my favorites...
Platformers/Arcade...
Bubble Bobble - port of the arcade. Different, but still plays well.
Rainbow Islands - another port, but a lot more different than the original. Actually it's kind of nice, but sort of difficult.
Castlequest - it's a puzzle and platformer mix. You collect keys to open doors. Not easy as it sounds since the game is big to explore!
Puzzles...
Tetris 2 - nice puzzle game, nothing relating to "tetris"
Dr.Mario - classic Nintendo's puzzle game.
Kickle Cubicle - very fun puzzle game involving creating new pathways.
Solomon's Key - While it could also be a platformer, it's really a nice to try.
Odds and Ends that are worth trying.
Clu Clu Land - Gets repetitive, but two players is a nice touch.
Rollerball - If you play two players, it'll be frantic.
Metal Storm - Short, but very fun platformer.
Milon's Secret Castle - Sort of challenging (unless you find the way to continue) platformer, but you need to get instructions to start you off.
Mighty Bomb Jack - unless you are aware of the arcade version, it's not bad. Personally, I enjoy it.
M.C. Kids - if you look pass the obvious endorsement, it's a nice platformer. Does actually get a bit challenging as you progress.
I can actually go on. I love my NES.