Terranigma and Illusion of Time/Gaia.
Why these, well it's mainly the music and the storytelling that got me hooked back in the day. The graphics are also drawn pleasing to my eye. I still feel with the characters when they go through tragedies, joy or heartache.
A Link to the Past has a lot to offer in terms of different weapons, but the lack of leveling and numeric stats usually let me rather put it into the Action-Adventure subgenre, similar to the Metroid series.