Shin Megami Tensei
One of the greatest and most well known RPG series started on the Super Famicom with Shin Megami Tensei. Released on October 30th 1992, Shin Megami Tensei is based off the novel Megami Tensei. Set in a more modern world than most RPGs, SMT features first person dungeons reminiscent of Phantasy Star and a contemporary story line. Quite a bit different from the swords and sorcery RPG style that dominated back then.
This game has been translated into English and has had a patch applied which fixes a few issues such as names and a couple bugs. If you're looking for something a bit different Shin Megami Tensei should be at the top of your list of games to check out.