Did somebody say obscure DS games?
I see Etrian Odyssey has been listed among the games recommended here. At its core, the series is a love letter to RPGs of old -- your adventure in the labyrinth with cardboard cut-out characters you mold, held together by a shoestring plot, with blisteringly difficult enemies and you draw your own maps. Get it if you feel adventurous.
I'm a little surprised that no one has recommended 999: Nine Doors, Nine Persons, Nine Hours. You need to pick this up. A great visual novel that doesn't hold back on its description of what's happening in-game. I also recommend picking up Zero Escape: Virtue's Last Reward for the 3DS. It falls in with 999, but can be played on its own without prior background knowledge of the previous game.
The Trauma Center games are awesome, and you should pick at least one of them up if your willing to shell out a little for it. I also highly recommend Ghost Trick: Phantom Detective. Ghost Trick comes from the mind that brought us Ace Attorney, but instead of being in the courtroom, you help a character named Sissel investigate his own murder, and help to prevent others.
Monster Hunter tends to run in the niche genre, but has a rich online community. You can team up with other hunters, or solo the game on your own. Monster Hunter 3 Ultimate for the 3DS and Wii U is an updated port of Monster Hunter Tri for the Wii, but has added quite a bit of new content.
Rune Factory used to be somewhat of an niche title, but ever since Rune Factory 4 appeared on Club Nintendo's Fan Favourites list for 2013, the series have been thrust into something of a mainstream light. That being said, I would recommend them. It's a bit of an unique experience -- Rune Factory mixes farming with RPG elements and light dungeon crawling.
Getting onto the mainstream topic a little further, if you plan on picking up Final Fantasy IV, might I suggest skipping over the DS version and go for the PSP version instead? Yeah, FFIV on the DS might have 3D and voice acting, but the PSP offers not only the original story, but an interlude story and a direct sequel called "The After Years," though it uses 2D based sprites. It all depends on your preference though. (And yes, I recommend getting this game either way because this game was amazing for its time.)
If I can think of any more lesser known games, I'll edit this post.