Ho boy... the list for the DS is quite long and I think people will eventually fill you in with the good stuff. As for the 3DS, the list is a lot shorter (obviously), so here we go:
Kid Icarus Uprising
A lot of people complained about the controls but really, I've never had any problems... if you try it for yourself, you're in for a really fun "God of War PG-rated edition". Colourful and fun art design, INCREDIBLE soundtrack... seriously, it's just mind-blowing arrangement after mind-blowing arrangement, really good voice acting and honestly the best 3D yet. Also, a really great online-multiplayer support with surprisingly in-depth combat and countless strategies. Must-have.
Kingdom Hearts: Dream Drop Distance
If you're even mildly interested in KH, it's a) a great recap and b) fucking fun. Seriously, the flowmotion movement system is amazingly fun, the sounds and graphics are amazing and it has a great game feel to it. Yeah, the story is some sort of blob by now, not impenetrable, but weird and annoying at times.
Mario Kart 7
Yeah, it's really good. Aside from that, it's Mario Kart, probably heard of it before.
Legend of Zelda: Ocarina of Time
Yea, it's still good. I like it.
Resident Evil: Relevaitions (typo intended)
IMO the last atmospheric RE but that might be because of the slightly claustrophobic setting and the fact that I exclusively played it late at night with the lights of and under my blanket. Still, it's really nifty.
Final Fantasy Theatrhythm
I like FF music and I'm a sucker for rhythm games but I can see that this game has pretty much only niche-appeal.
On the eShop there are three games/apps that are really good:
Dillon's Rolling Western
Nintendo's stab at a tower defense game and it's fucking AWESOME. Tight controls, action-y input, nice western soundtrack (albeit a bit repetitive because it has fewer songs). Hours upon hours of fun.
Pushblox/Fallblox
great puzzle game with an extensive editor mode included. really getting your money's worth out of this.
Colors 3D
wonderful drawing app that let's you draw 3D pics. if you're artistically inclined, it's a really fun toy to scribble with. Has decent online support for posting your art works as well.
I missed a lot of games that are good (the entire plethora of mario games is decent enough for example, Tales of the Abyss, the new Professor Layton, Paper Mario, etc) but I chose to focus on the ones I really, really enjoyed.
Also with Fire Emblem Awakening coming out in a couple of months, I really got quite a few enjoyable hours out of the 3DS.
