Alice in wonder dream
Whoa ho ho, this topic is for the
best Japan-only games, not the
rest.
Here are four suggestions that have not been mentioned already:
Mr. Heli no Daiboken
Atomic RoboKid Special
-both games are similar, but excellent side-scrolling free-roaming shooting games. I think Mr. Heli is a slightly better game, but it's much harder with some severe difficulty spikes, whereas RoboKid is longer and more accessible, making it easier to dive into the action. If you like them you might like the overhead tank game, Metal Stoker.
Brandish
-despite being a dungeon-crawling top-down RPG, nearly every important function is labeled in English, and items are displayed as visual icons making it easy to shop for potions, swords, etc. Game is very tough to get in to and has a laughably dumb camera-angle switching system, but if you consult Digi.k's nice topic covering the basics, you will find yourself playing a very rewarding game.
Genpei Toumaden Kannoni
-Yeah I know it was released in the west as Samurai Ghost but listen up: it's one of the top action games on the system, has no need of the English language (the western port certainly didn't, considering its garbled translations), and if you can figure out how the game controls, you'll find it to be one of the most satisfying games on the system. Tricky boss fights, lots and lots of stages, and easier to control than its JPN-only predecessor, Genpei Toumaden. That being said, I really like Genpei Toumaden and think it's one of the coolest 80s games out there - but I have only played the arcade version, and not the PCE port. Others will have to vouch (or not) for how the PCE port is.
Travel Eple - cute lil penguins in a Bomberman type of game
Cute as they may be, I have to disagree with this one. The enemy AI in this game leaves so much to be desired, and the game knows this because it compensates by having enemies practically teleport on top of you if you move too far away. Bomberman is the clear winner of these arena battle-type games, and I'd wager 94 is the best of the Bombermans (haven't played the others though)