Chrono Trigger - Best RPG ever. Great story, great soundtrack, great battle system.

Final Fantasy VI - You can outrun and suplex a train.

Terranigma - Excellent story and gameplay. You play as a god who aids in the creation of the world and evolution, defeat all the evils and help humans advance. It has a really touching story and ending.

E.V.O. Search for Eden - IIRC you're a messenger of Gaia and sent to help animals evolve. The mechanics are really interesting because you can freely evolve different parts of your body to any animal's part that's available during that time period.

Super Robot Taisen - Gundams, Getter, Mazinger and your favorite mecha series all in one game. It has the best attack animations in any SRPG ever.