1) Super Mario Bros. 3 (by far the best NES game I ever played)
2) Teenage Mutant Ninja Turtles 2 (multiplayer was a total blast)
3) Chip and Dale: Resue Hunters (too easy, but highly enjoyable)
4) Nintendo World Cup Soccer (used to love those crazy bicycle kicks/volleys)
5) Super Off Road (awesome racing game, I remember it as hard to beat too)
Honorary mention: Super Mario Bros. The first videogame I ever beat, still remember where I was when it happened.
Obviously I missed out on some great ones when I was a kid. I never played Zelda, FF or Castlevania on the NES. My first experience with those franchises was when I got my SNES in 1993.