Contact
Contact is often compared with EarthBound, but it should be noted that the similarities are strictly thematic (e.g. the Andonuts professor Sean mentioned); as for how the game plays, it's very different and somewhat non-standard. I'd actually note Secret of Evermore as an inspiration for that department, but let me elaborate.
The combat system in Contact is in real-time, ala your everyday dungeon crawler. You move the game's boy hero, Terry, through beaches, caves, hidden military installations, et al., and enemies (which range from unfriendly snakes to missile-launching robot sentries) roam about just waiting for a good battle. By pressing the 'B' button, Terry toggles between Battle mode - he pulls out his weapon, and moves slower than normal - and Passive mode, which is used for typical movement and/or running away when necessary.
In Battle mode, normal attacks happen automatically and periodically. But you can also trigger special abilities, or consume food, or try to move about to dodge attacks, on command. While at first glance it doesn't possess the complexity of a more traditional menu-based RPG, there are a lot of more subtle options available through movement and items.
One of the more interesting aspects of Contact is the experience system. Though Terry does level up, it's not in the way you'd expect, becoming more heroic with every slain foe - experience points are earned for specific abilities or attributes based on how often they're used. There is a great degree of separation, but not so much that it's too hard to follow; for instance, the more you attack, the more your physical strength will level up, but there is also a level for each type of weapon (sharp, blunt, or fist). There are levels for each of the four elements in attack ability and in defense ability, which will go up as you use or are hit by an elemental attack, respectively. There's even a level for how fast you walk (which levels up slowly as you cover more ground). The net effect is that Terry doesn't just get better, he gets better at the things he specifically does, which is both more believable than a single character level, and more interesting to configure.
Cooking plays a big part in Contact. Fairly early on, you sail onto the island of a naked chef, who grants you the ability to cook dishes at bonfires or in your ship's kitchen. You start out an absolutely terrible cook, but as you attempt and create more dishes, results begin to become consistent. And, far from being a tertiary aspect of the game, Cooking is by far the best way to get invaluable health-restoring items.
As I compare Contact to Secret of Evermore, I must mention that in the deeper labyrinthine dungeons, it is similarly disorienting and difficult to navigate. But, Contact has a clever solution to this too. When your HP drops to zero, Terry goes "out of commission" and must be resuscitated back at the ship; but, other than your physical location, everything else is preserved (that is, the experience levels and items you picked up before you died). It gives death just enough inconvenience to make it unappealing, but at the same time marginalizes lost progress, which is a great encouragement to keep going despite it.
There's a lot more to Contact, too, like ability-enhancing costumes and a superb fourth-wall plot, but I'll get on those later. Suffice it to say, this is quite an impressive little game card.
Progress: 3 Power Cells