Chrono Trigger is an RPG by Square, where the main character, Crono, spans time to fix history and save the future from the alien life-form that fell to earth in the prehistoric ages.  This game features turn-based fighting that occurs in the same setting where general navigation occurs. It also lets you control the main character and his companions.  The are lots of places to travel in the world.  There are thirteen different endings to the game.  

The artwork is by the same artist, Akira Toriyama, that did Dragon Quest and Dragon Ball.  I love this art style in games, it is really easy to draw them in an 8- or 16-bit system.  There is strong influence from Final Fantasy and Dragon Quest, but it is still a game all its own.  Square really understands how to make a great RPG.