A classic that you've probably never heard of
One game that never garnered much attention, (possibly because another of Enix's offerings called Actraiser; you may have heard of it) but was as amazing as the rest of the early line-up, was none other than Soul Blazer. In it, you control an angel that is sent down to rescue mortals in all shapes and sizes -- people, plants, animals, and their homes. To do this, you defeat groups of enemies that spawn out of glowing red portals. When they are all defeated the portal turns green and upon standing on it, it frees a denizen of the particular areas (or opens up something in the dungeon you're exploring).
With you is the spirit of certain creatures that floats around you, with each spirit having a different ability (like shooting a fireball, casting light upon dark areas, etc). These come in handy and are often needed to solve environmental puzzles as well as defeat enemies.
While the game had its roots in adventures of yore like Legend of Zelda, Soul Blazer had a lot of original concepts and was executed very well. On top of that, it had great graphics and sound to back it up. The plots for each area were well-writen and drew you in, and as the story developes you realize they are all intertwined. It wasn't particularly hard, but it still gave plenty of hours of gameplay and moved along at a smooth pace.
The biggest problem Soul Blazer had going for it was a lack of a fanbase like many of the other titles released at the time had, and perhaps it was hiding in the shadow of Actraiser (which, personally, I enjoyed far less). It's a bit disappointing that it never got the recognition (or legitimate sequel) it deserved, but at the same time it felt like a secret treasure that only a few of us knew about and it was ours. All ours.