I'm deliberately not listing any ports/any sequels. And I'm leaving out the usual recommendations of The World Ends With You...and the like...
DS:
- Aliens Infestation (late to the NDS life, it's like Metroid and the Aliens franchise had a love child, and then threw all the difficulty at you. The first boss is terrifying, the game keeps the mechanics creepy, and it's the one DS game that actually captures the essence of being lost on a ship, and there's a terrifying life form on it that wants to eat your face).
- Dragon Quest Heroes: Rocket Slime. A game with simple mechanics, control a slime/flan to hit things, and then carry things/more slimes back to the village. Eventually turns into mecha battles with your slime literally chucking stuff at the other mecha (you gather this stuff in the earlier stages). You eventually wear down your opponents, and then you can launch yourself out of the mecha to invade the mecha and take down the core. It is very satisfying. (Also, there is a Japanese sequel on the 3DS...I wish that there was an actual official release here.) [Note: I know there's a group here working on a fan translation...continue that work, please!]
- Dragon Quest Monsters: Joker. Fun game with Pokemon like battles. Unfortunately, the wifi support is gone now, but you could have had networked/leaderboard battles with other real players. The story is pretty interesting and the higher level monsters are great too.
Edit: (Forgot one!)
- Duck Amuck. Remember Daffy Duck? Your goal in this game is to piss him off until he rants and raves like a crazy lunatic. The animation is gorgeous and the more you play with it, the more reactions you get out of him. It's another mini-game collection with some REALLY bad ones in there, but you just have to experience it because it's just odd...
- Feel the Magic. One of the weirder launch games for the DS. It's essentially a mini-game collection, with a LOT of Japanese weirdness attached to it. [Warning: some of the later sequences get a little PG-13...] You essentially play a guy who notices a cute girl in the background and then decides to join a performance group to get her attention. You complete mini-games to boost up a meter, and eventually, win her affection.
- Lunar Knights. Vampire hunters and space battles. (Note: the space battles use the really annoying motion controls, and I always die with it.) It's a sequel to the Boktai series (hence the obsession with the SUN/Lunar cycles)...
- Retro Game Challenge. Mini-games, but packaged in a 8 bit computer/NES/Famicom style. Very fun, and very challenging at times. The English voices are annoying although.
- Soul Bubbles. Toys R Us exclusive back in the day. Basically use your stylus to guide a bubble around a level. It's a good game, and I wish I bought the actual physical copy back in the day. Oh well...it didn't sell well enough that people noticed it.
- Tingles Rosy Rupeeland. I know! I know. It's majorly weird, but it's one of the reasons I bought an Acekard 2i back in the day (cost me $50 bones and a lecture from my dad saying that you shouldn't buy shit from people you don't know). Go play it. You play as Tingle, who lives in "seriously not Hyrule" and everyone is a greedy asshat who needs rupees. Your goal is to gather all the rupees you can. The art style is off-putting to some, but it's an unique and weird title. (Also, the "secret" ending is seriously...weird.)
- Trauma Center. Touch screen based surgery game. Very fun, and very much one of the games I wished I had a physical copy of it.
3DS Games:
- Steamworld Dig. Dig through layers of dirt with your upgrades, finding ores and valuables along the way. You also find upgrades inside "mini-dungeons". Very good, although there's not much replayability as the "mini-dungeons" still feature the same puzzles.
- Gunman Clive. I prefer the first one, as it feels like the more "complete" experience without any other additions. It's a simple platformer with no lives system. It works as you die and can retry the level as many times as you want.
- Attack of the Friday Monsters. It's a visual novel style game. It works well, and you get to solve a mystery of why in the world monsters come out to play every Friday night.
- Cartoon Network: Battle Crashers. Take six popular shows, mash them together to create a beat 'em up with each character having specific powers and attacks to clear stages? Yes please. The boss battles are fascinating in a weird way.
