Well, there are tons of fun games, but here are some popular ones:
1.
Ankoko Densetsu -- Billed as "Legendary Axe 2" in North America, this a great hack-n-slash platformer. There is a wee bit of exploration the first time through, but when you replay it, you'll probably follow the most direct paths through the game. One of the best, brooding HuCard soundtracks and a somber atmosphere / aesthetic to match it (I love the stage with lightning...). Excellent game, all around, with interesting bosses. Plus, for a game with minimal storyline, there's a plot twist!
2.
Narazumo no Sentou Butai Bloody Wolf -- Again, a great soundtrack. Aside from some slowdown, this is a gem. Nice, albeit generic, selection of weapons (although you do get to ride a machine-gun-equipped motorcycle!) Personally, I like the fact that you can jump in this game (adds a *tiny* dash of platforming to certain segments of the game). A variety of stages with different objectives keeps the game interesting (from all-out action on a raft to methodical exploration of a large prison camp to free prisoners). Again, for a game with a minimal storyline, there's a great plot twist... Hmmmmm, there seems to be a theme with my mini-reviews...
3.
Soldier Blade -- If you dig horizontal shooters, check this "installment" of Star Soldier. I like all of the Star Soldier games, but most folks claim SB is superior. It's a great game, regardless.
I'll stop there...