Of course Metroid, Legend of Zelda and Kid Icarus are always the classic "must have" titles but try to find a game called "Kickle Cubicle". It's a weird little top down action puzzle game that I probably played nonstop for a good three months as a kid.
I really can't recommend the Megaman series enough.
It gets a bit squirrely around Megaman 4 but the entire core series is worth picking up and playing.
I would avoid anything branded so just say no to any comic book, movie or TV show related games. If you think movie tie-in games are bad these days they've got nothing on the terrible games from the 8-bit days.
The only exception to this is the Capcom produced Disney collection.
(Duck Tales, Rescue Rangers, Darkwing Duck etc.)
Now that I'm actually browsing through my collection I can also recommend Adventure Island, Alien Syndrome, Contra, Gauntlet, Marble Madness, Mike Tyson's Punch-Out, River city Ransom, Rockin' Kats and Star Tropics.
