Lufia II: Rise of the Sinistrals (Super Nintendo, 1996)

Everyone knows about Final Fantasy 2 and 3, Chrono Trigger, and Zelda, but Lufia 2 is hands down the best game on SNES. The graphics are the equal of the rest, the soudntrack amazing and the characters wonderful and endearing. The story is excellent also, and even though it is the second game in a series, it is a prequel and requires no knowledge of the previous game. The game play is heads and shoulders above the otehr games, as it offers tons of variety. You face random battles on the map screen, but you see the mobs before the fight in dungeons(like Chrono). There are tons of puzzles in this game, many of them ridiculously difficult, so you don't always just hack and slash. This game is one of the few must own games on the SNES.