Sweet Home, Little Nemo: The Dream Master, Live A Live, Muramasa: The Demon Blade.
Sweet Home...well, I'm not sure how popular it is in Japan, but that's where it stayed. As a grim, gore-y game in the 80s, it would have been butchered in pre-ESRB censorship. It's a Capcom survival-horror RPG on the famicon (NES) that is based on a movie. One of the best horror games I've ever played. It has a mysterious story with a very sudden delivery. There's only a couple exposition-heavy scenes in the game. The rest is just old notes and hidden messages. The fast-paced turn-based combat helps too. You know how getting a gun that blows apart your enemies in one hit kind of ruins the atmosphere? In my experience, bigger numbers don't have the same effect as bigger guns. The lack of real combat animation or victory fanfare helps too...you never feel like a badass. Ever. For a horror game, that's perfect! This might just be my favorite Capcom game.
Little Nemo: The Dream Master...another licensed NES game from Capcom. This time, it's a wonderland-style adventure into a magical world. You play as a small, fragile child who befriends passive animals with candy and, depending on the animal, either rides them or wears a Mario-style suit (that possibly pre-dates Mario 3. I'm not sure). How fragile is he? His only attack is a stun, and the "friendly" animals can hit you before you bribe them with enough candy. I picked this one up for $5 at a Top Games today, and I'm loving every magical, excruciatingly difficult moment.
Live A Live. Another Japan-only RPG, this time for Square. Live A Live was released on the SNES (Super Famicon?). It's sort of Chrono Trigger's predecessor, but instead of time travel, you play multiple characters in shorter story arcs that make up a world's history. I started with a robot on a ship with some horror elements, now I'm playing a cave man who communicates through slapstick. I've only just started, but it's really intriguing.
Muramasa: The Demon Blade. The go-to response whenever someone claims there's nothing worthwhile on the Wii that wasn't made by Nintendo (and/or Capcom, Konami, Sega, etc.)
Here, look!