Well, people already recommended excellent games, but im going to recommend a game from visual novels, which is basically a book, but that is excellent:999(For DS) and Virtues Last Reward(for 3DS).Both from the same franchise, being 999 the first game, and Virtue the second, they are superb!Recommended to anyone.

I'l recommend stuff that I don't see in others list.

DS

Ace Attorney games.
Okamiden
Kirby games
Hotel Dusk Room 215
Trace Memory
Advance Wars games.

3DS

Code Name STEAM

Some digital ones: 

Pushmo series, Sakura Samurai, Box Boy!, ect.

I see others have beat me to the 3DS games

A bit off topic but why do the DS games still cost so much? I would think they'd be cheaper by now, but they are still awfully high in price.

The right stick on the N3DS XL is garbage. Go ahead and dismiss any dreams of using it for an fps of tps.

Fun fact: my autocorrect just turned "tps" into the word "God"

With that said, here are my picks:

The Legend of Zelda: Ocarina of Time 3D
Super Mario 3D World
Advance Wars DS
Resident Evil Revelations
Mario Kart 7
Super Street Fighter 4
The Legend of Zelda: Link Between Worlds
Chrono Trigger
Pokemon Y
New Super Mario Bros 2

DS:
Super Princess Peach (:D)
Pokemon Platinum
Pokemon SoulSilver/Heart Gold
Mario And Luigi: Bowsers Inside Story
Pokemon Conquest
Pokemon Mystery Dungeon Explorers of whatever
Kirby Super Star Ultra
3DS:
Link Between Worlds (Highest recommendation)
Etrian Odyssey Untold
Majora's Mask
Resident Evil Revelations
Bravely Default
Tomodachi Life
Shin Megami Tensei 4
Fire Emblem

3DS:

- Fire Emblem Awakening
- Bravely Default (YAAAAAAAAS)
- Pokémon Omega Ruby/Alpha Sapphire
- Pokémon X/Y
- Super Mario 3D Land
- The Legend of Zelda: A Link Between Worlds
- Super Smash Bros. for Nintendo 3DS
- Luigi's Mansion: Dark Moon
- Animal Crossing: New Leaf
- The Legend of Zelda: Majora's Mask 3D

For all those people that mentioned DS games and didn't include Ghost Trick: you deserve a kick in the crotch area. >:[

How could I forget Ghost Trick, I'l punish myself later.

Guys, how has no one mentioned any Etrian Odyessy games or Ace Attorney games? What about Persona Q? Codename S.T.E.A.M? Anyone? 

Edit: How the heck did I miss all those Etrian Oddyesy and Ace Attorney games? Anyway, Metroid Prime Hunters and Goldeneye 007 are good FPS games for the DS.

3DS:
Fire Emblem Awakening
Pokemon X and Y and Pokemon ORAS
Kid Icarus Uprising
Bravely Default
Animal Crossing New Leaf
Fantasy Life
Super Smash Bros for 3DS
Luigi's Mansion Dark Moon
Tomodachi Life

Future titles to look out for:
Fire Emblem Fates
Mario and Luigi Paper Jam
Yo-Kai Watch
Bravely Second End Layer