Can't berlieve I just discovered this thread. Here are some games I have beat without using a continue, or dying.
Zelda
Castlevania 1
Kid Icarus
Super Mario 1 (easy)
Punch-Out
Kung-Fu
Duck Tales
Rescue Rangers
River City Ransom
Double Dragon 2
Faxanadu
Rygar
That's just some. I'm sure there are more, just off the top of my head.
Here are some hard games I have managed to beat, and am happy with not having 1cc.
All the Ninja Gaidens
Ghosts n' Goblins (2nd run with shield)
Battletoads
Shit I can't beat.
Soloman's Key (so close)
Legacy of the Wizard
Festers Quest
Bart vs the Space Mutants (again so close...)