Wow, this is going to be tough for me...
1. The Legend of Zelda
2. Mike Tyson's Punch-Out!!
3. Super Mario Bros. 2 (USA)
4. Final Fantasy
5. Dragon Warrior
6. Super Mario Bros. 3
7. Contra
8. Tecmo Super Bowl
9. Blades of Steel
10. Nobunaga's Ambition
There are SO many games that could easily be on this list, and the numbering is mostly arbitrary. I tried to mix it up with a representation of adventure, platform, RPG, run and gun, sports, and strategy titles while also staying true to what I poured the most hours into.
Honorable Mentions: Super Mario Bros., Dragon Warrior 2-4, Ninja Gaiden 1-3, Double Dragon 1 & 2, Mega Man 1-6, Castelvania 1-3, Baseball Stars, Kung Fu, Jackal, Commando, Iron Tank, Batman, Faxanadu, Kid Icarus, Tetris, Ghosts n Goblins, Ultima 3-5, I'm sure there are others I'm forgetting...