Life Force - This was the first shmup I ever played. Developed by Konami, complete with the Moai heads.
Air Fortress
Monster Truck Rally
Darkwing Duck
Jackal
Formula One: Built To Win - Recommended if you enjoyed Outrun and Rad Racer, as it's similar to those titles.
Spy vs. Spy - This is especially fun in multiplayer.
Kings Of The Beach - Top-notch Konami Volleyball title (published under the Ultra Games brand). Another fun multiplayer game.
Guerilla War - Similar to Ikari Warriors.
Pin Bot - Pretty accurate simulation of the Williams pinball table - well, as accurate as you could pull off on an NES cart, anyways.
The Bugs Bunny Birthday Blowout - Kemco celebrated Bugs Bunny's 50'th birthday with the release of this platformer with a good amount of challenge.
Sky Shark - Like difficult vertical shmups? This is for you.
Tiger-Heli - Another overlooked vertical-shmup that's worth a try.
Tiny Toon Adventures - Another fun Konami title.
Remote Control - Decent quiz game, but only recommended depending on how well your knowledge of classic TV is.
Willow - An action RPG. Imo, this was better than the movie. Wish it had used a battery save instead of the long password system, though.
And not to play the "OMG! REPOST!" card, but here's a similar thread from a while back you might want to look through, as there's some other stuff that hasn't been mentioned yet:
The Definitive List of Great, Obscure NES Games