Tough call. The NES had a lot of great game that I used to play. In fact, it even had some random, obscure, and at times, odd, games that I would happen to play, just to play. Whether they be single player or multiplayer games. I don't know if I can pick just one. I might be able to narrow it down to a few, which might help. So, let's see what I can name off hand that I loved, and felt were great, and go from there. Tho, I'm going to leave off games that I feel were good, but not quite my favorite.. but let's see... I'm sure there are some obvious ones, so lets go with them first.
The Legend of Zelda
Zelda 2: The Adventures Link
Super Mario Bros
Super Mario Bros 3
Contra
Super C
Mike Tyson's Punch-Out
Mega Man 3 (I like 3 better than 2. Part 2 is good, but 3 is better)
Metroid
Blaster Master
Bionic Commando
Double Dragon 2
Bubble Bobble
Teenage Mutant Ninja Turtles 2: The Arcade Game
Super Dodge Ball
Tecmo Bowl
Ninja Gaiden
Battletoads
Final Fantasy
Excitebike
Rad Racer
Skate or Die
Castlevania
River City Ransom
R.C. Pro-Am
Ghosts 'n Goblins
Dragon Warrior
Batman
Bad Dudes
Little Nemo: The Dream Master
Chip 'n Dale: Rescue Rangers
Gradius
Tiger Heli
Jackal
1942
Deja Vu
Uninvited
Dr. Mario
Strider
Kid Icarus
Guerrilla War
Heavy Barrel
Marble Madness
Pin Bot
Major League Baseball (I still have that theme song in my head)
Solomon's Key
Rygar
Rush'n Attack
Star Tropics
Star Tropics 2: Zoda's Revenge
Willow
Donkey Kong
Galaga
Life Force
....etc.etc.etc.. I could keep going.
Well, that was no help, was it.
Hmm. Let's try to narrow just these down to 10, and see what happens.
The Legend of Zelda
Super Mario Bros.
Super Mario Bros. 3
Blaster Master
Contra
Bionic Commando
Mega Man 3
Punch-Out
Double Dragon 2
Castlevania
Metroid
Well, that's 11 right there. See, already failed at a Top Ten list. I could add more to this list, however, I'll keep these "Top Eleven" and say that these were some of the defining games of the NES. These are listed in no particular order. But, again, they pretty much defined the NES. Were there other great games. Absolutely. Were there other games that I liked, even tho they weren't great. Again, absolutely. However, I think if I were to introduce somebody new to the NES, I would most likely start with these 11, and go from there.
Picking an absolute favorite is almost impossible. There is such variety and diversity, and so many great games, that it's truly difficult to pick just one. So, for now, I'll leave it at the Top Eleven for you. Enjoy.