Just my personal list:
PAL exclusive: Mr. Gimmick
Famicom exclusive: Splatterhouse
Homebrew/Zapper: Super Russian Roulette
Platformer: Super Mario 2
Lesser known sidescroller: Shatterhand
Game of mini-games: California Games
Football: Tecmo Super Bowl
Baseball: (tie) RBI Baseball/Baseball Stars
Hockey: Ice Hockey
Best 2 player game: probably one of the above sports games or Contra
RPG: Crystalis
Shooter: Lifeforce
Arcade/high score: Burgertime
Hardest: ghost and goblins
Easiest: Felix the Cat
Best music: Mega Man 2
Racing: Micro Machines/Excitebike