I'm playing right now the Ace Attorney saga

Enchanted Folk and The School of Wizardry; GTa Chinatown Wars; Jump Ultimate Stars; The World Ends With You; Yoshi's Island; Kingdom Hearts 358/2 Days and of course, Pokemon Mystery Dungeon.

Hotel Dusk is a great game too.

Retro Game Challenge - Not really well known, based on Japanese show with the same name(in Japan called Gamecenter CX). It's a compilation of Famicom stylized games. For every game you get few challenges to complete. You also collect magazines with cheats and stuff like that. Feels like 80s/90s, pretty neat game.

Jump Ultimate Stars - Unusual fighting game released only in Japan. It plays a little like Super Smash Bros. It has many characters to play as - all from Shounen Jump manga, so you'll get to play as characters from Naruto, Bleach, Yu Yu Hakusho and more.

Picross 3D - Picross in 3D. Simple and fun.

Elite Beat Agents - Great rhythm game with nice songs. For every song you get a little story of someone who needs help, and you hel him by dancing. Awesome.

Space Invaders Extreme - Space Invaders with awesome music.

Contra 4 - WayForward does it again. One of the greatest DS platformer, hard and fast, like Contra game should be. It takes some time to beat it, especially on hard difficulty. Plus it has great music.

N+ - Ever heard of this little flash game? If not, go look for it and play it. DS version have some stuff added, it's simple and fun to play. Plus, it has level editor and you can exchange levels via Wi-Fi, so you'll never run out of levels to play.

Art Academy - Nice "game" if you want to learn a little about drawing and painting. Nice for beginners, but don't expect to get good at drawing with this game alone.

Inazuma Eleven - Soccer? RPG? Amazing special shots? This game has it all! Incredible number of players to recruit, addictive gameplay and actually interesting story. Has a sequel.

Well, that's all for now, maybe I'll remember some more later. Have fun.

Don't know how popular they were, but I loved the Etrian Odyssey games.

Plants vs Zombies was pretty entertaining :P

what about radiant historia?

And also Lunar Knights

i enjoyed the custom robo for DS and this other mech fighting game in which the touch pad let you shoot your crossbow/guns etc. Dont remember what it was called because it was heavily japaneese - A mate use to have em.

What about Suikoden Tierkreis? That's a nice RPG too

Megaman StarForce series before that Battlenetwork

I think the only non-popular DS Games I enjoyed were "Monster Rancher DS" and "Trauma Center: Under the Knife". All the others DS games I played could be considered popular. ;_;

Don't play DS but really loved Chinatown Wars on my psp! It's my second favorite GTA game behind San Andreas.

Both of the Dementium games are pretty fun, never really got popular sadly. Nice survival horror like first person shooters that make you aim carefully and decide when to fight or not. They can be really frustrating though.

Moon, another FPS by the same developers as Dementium, is pretty darn fun for at least one play through.

Been awhile since I've touched the old original DS...

Hotel Dusk! still wanting to import the sequel :D

FORGOT ABOUT SOMA BRINGEEEEEEEEEERRRRRR

Boing docomodake :)

Suujin Taisen (Japan only, but it has a version on DSIware)
Monster Rancher DS
Trauma Center
Digimon World Championship (I'm not a fan of the series)

i only ever got a DS to play pokemon... :P

999: Nine Hours, Nine Persons, Nine Doors
Ghost Trick: Phantom Detective
Rhythm Heaven
Elite Beat Agents
Knights in the Nightmare
Hotel dusk: Room 215
Freshly-Picked Tingle's Rosy Rupeeland

After quickly checking what others have suggested I didn't see two games I enjoyed playing:

Mystery Dungeon: Shiren the Wanderer - Roguelike, can be really unforgiving but that just makes it more fun to play.
Contact - Not the greatest of games, but I enjoyed it due to the story and it's quirks.

I dunno what's "popular", I just play what I like. But most of these games are very popular in particular circles. SMT has super fanatics, but "average gamers" will have not heard of it, or at least never played one.

Etrian Odyssey series (Like II the best, but probably the rarest - also probably "Popular")
Shin Megami Tensei: Devil Survivor 1 & 2
Shin Megami Tensei Strange Journey
999
Shiren the Wanderer
Suikoden Tierkreis
Retro Game Challenge
Knights in the Nightmare
Radiant Historia - probably "popular"
Okamiden
Ghost Trick
Hotel Dusk
The World Ends with You - since you said you like this I think you'd like SMT Devil Survivor 1
Dark Spire

Lots of these are pretty long games, so hopefully you have transit/job/school something that warrants staring at the small screen :)

Well I don't know if thats popular but I suggest you to play Yu-Gi-Oh World Championship series.I finished some of them on emulator and I think they're awesome.

Hmm. Hard choice, because many of the games I like on DS have gotten well known.

Dragon Quest Heroes: Rocket Slime / Dragon Quest IV: The Chapters of the Chosen are both part of the Dragon Quest series.
Ghost Trick is known as a game from the same people behind the Phoenix Wright series.
Nine Hours, Nine Persons, Nine Doors has gotten popular and even received a sequel.
Pokemon games, well... Pokmemon.
Both of the Sonic Rush titles and Sonic Colours are the same.
Spider-Man: Web of Shadows is another well known series, though this is damn awesome considering most of the rest are licensed crap.

This is pretty difficult.

I know! The Trackmania games. :D

KINGDOM HEARTS :D

but you should play the ps2 games first. or it wont be super awesome

Yu-Gi-Oh! GX: Duel Academy

Disgaea! And Rune Factory 3.