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Super Mario World. Launch title, best selling game on the system.
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Donkey Kong Country. Helped revitalize the old hardware to appear to compete with newer systems.
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Street Fighter II. Counterpoint to the Genesis Rushmore. Best selling third party game on the system.
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Chrono Trigger. I think an RPG is a must for the Rushmore. FF4 (and arguably 6) is better on other systems, the Seiken games and Ogre Battle aren't popular enough, and Earthbound wasn't loved in its time.
HMs: There are tons of great games, but only two that I considered seriously: Super Metroid and Mario Paint.