I have a few of these games, actually.
Danganronpa Series - This isn't quite so obscure now, mainly because of how much I gush about it on sb and the the anime series, but it's still a series that doesn't often get talked about. It's a vita exclusive series that's kinda like Phoenix Wright, except with more mini games thrown into the court sessions. It's an extremely well written murder mystery series that's dark, comedic, and action packed all at once.
Adventure Time: HIKWDSOG?! - Adventure Time: Hey Ice King, Why'd You Steal Our Garbage?! is an amazing game based on the Adventure Time series (duh). It's a Zelda 2 clone, which already makes it unique from most other games. You explore Ooo, meet wacky characters from the show, and partake in an adventure of epic proportions; to get your garbage back after it's been stolen by the Ice King! It's packed full of references to the show, it doesn't take itself serious, the music is amazing, and while the game is short, I've replayed it so many times. And it's a Zelda 2 clone. Can we just take a second to acknowledge how awesome Zelda 2 was? More names need to be like it. I loved this game so much, I immedately bought the collector's edition for the sequel, Explore The Dungeon Because I DONT KNOW!!!. I regret that choice to this day because God that game sucked, but I'm getting off topic here. Adventure Time: HIKWDSOG?! is awesome.
Parappa the Rapper series - This series of rhythm games stars a paper thin dog named Parappa, and the many misadventures he has trying to win over his crush, a flower named Sunny Funny. The songs are all great and extremely memorable, and the gameplay is fun. Sadly the series never got a third installment, but hope remains eternal. And if you do like the two games, there's a spinoff called Un Jammy Lammy. It's set in the same world, but this time you control Lammy, a guitar who tries to get to a concert in time but ends up going on a weird quest helping put babies to sleep, cutting down trees, and even going to hell.
Seriously though, the music is great. Just listen to it