I'm trying to finish up my DS collection before 3DS starts getting good stuff.
I want to make sure I didn't miss any essentials.

^We do have a DS recommendations thread. You could always post what you have there and we can tell you what you're missing.

Anyways, on topic, in no order:

Retro Game Challenge
The Dark Spire
Shin Megami Tensei: Strange Journey
Meteos
Chrono Trigger
Dragon Quest Heroes: Rocket Slime
Pokemon HeartGold
N+
Shin Megami Tensei: Devil Survivor
Lunar Knights

1. The World Ends With You (Easy one for me here. So unique and a wonderful story. Pin grinding, post game is the only thing I didn't like but oh well)
2. Lufia: Curse of the Sinistrals. A wonderful remake. I'm amazed how the game is still fantastic even though they turned it into an action RPG.
3. Radiant Historia. Amazing story and creative battle system. The story just gets better and better.
4. Elite Beat Agents. Wonderful game and can usually be found somewhere between $5 and $10. One of the most addictive games I've ever played and a great game to play in short bursts.
5. Ghost Trick Phantom Detective. Amazing game and incredible story. The puzzle system where you possess and interact with objects makes the game really fun. Only reason its not ranked higher is there is almost no re-playability factor. Still though this game is awesome.
6. GTA Chinatown Wars. It's like the old GTA games but much more polished, a ton of missions and a lot easier to get annoying cops off your *ss. Some funny dialog too. The missions are the best aspect of this game though imo.
7. Mario and Luigi: Bowser's Inside Story. Some may have this ranked higher but considering the games short length and how easy it is, I just didn't feel there was quite enough content to be higher. A great game though still. Great dialog like all M&L games and the battle system is very creative.
8.Dragon Quest: Rocket Slime. I'm pissed that I can't find this game right now but despite that it's still fun. The platforming probably ranks from alright to good, but the tank battles alone in this game are amazing. They alone are enough to purchase this game.
9. Final Fantasy Fables: Chocobo Tales. Yes its cutesy and yes its a minigame collection, but its actually really fun with a fun little side card game. Don't let the nauseating cuteness detract you from this gem.
10. Final Fantasy: The 4 Heroes of Light. One of the best Final Fantasy games I've played in quite a while. If you want a challenge too, this game is it. It is also easy to get into without a lot of hand holding.

Hope this helps. Also close to 10 but honorable mentions from me are Dragon Quest IV and Fire Emblem Shadow Dragon. Despite its lack of story its still FE goodness.

This is a list of my favorite games that aren't Mario or Pokemon games in no order:
Viewtiful Joe: Double Trouble
Rhythm Heaven
Warioware Touched
Professor Layton and the Unwound Future
Contra 4
Worms Open Warfare 2
Looney Tunes Duck Amuck
Elite Beat Agents
Phoenix Wright
Okamiden

RGC
BIS
MMZC
N+
Super Scribblenauts
WarioWare DIY
Mario Kart DS
Pokemon Diamond/Platinum (they're practically the same)
LEGO Star Wars: The Complete Saga
Shaun the Sheep

Also, clever way to ask for recommendations but not get your topic locked.

I dont have it but
999

That's not ten games; it's 999 (ba dum pish!).

1. Pokemon Black and White- the most addictive Pokemon yet.
2. Warioware: Touched!- brilliant uses of the system and perfect for any length of playtime.
3. Mario & Luigi: Bowser's Inside Story- nowhere near as good as its GBA grandpapa but a great game nonetheless.
4. Pokemon Heartgold and Soulsilver- the games that really got me into Pokemon.
5. Kirby Super Star Ultra- a great game for score-attacks.
6. The Legend of Zelda: Spirit Tracks- the most accesable Zelda yet.
7. New Super Mario Bros.- I like the Wii version better, but the original still rocks.
8. Warioware DIY- Lets your mind run on the loose.
9. Bleach: Dark Souls- Hyper-fast fighting action (even though I deeply suck at it).
10. Animal Crossing: Wild World- A life-consuming gem.

1.) Pokemon Black and White
2.) Pokemon Heart Gold and Soul Silver
3.) Legend of Zelda: Spirit Tracks
4.) Pokemon Platinum
5.) Super Scribblenauts
6.) Kirby Super Star Ultra
7.) Super Mario 64 DS
8.) Mario Kart DS
9.) GTA Chinatown Wars (Left it behind when I visited family in another state and miss it greatly. )
10.) Mario and Luigi: Partners in Time: The idea of fighting evil with your younger self is just so awesome!

Honorable mentions:
Rythm Heaven
Legend of Zelda: Phantom Hourglass
Mario and Luigi: Bowser's Inside Story
New Super Mario Bros. DS

ok ill add more
Pokemon Black
Pokemon HG
Ouendan 2
Daigasso Band Brothers DX
TWEWY
Dragon Quest 9
Zelda Spirit Tracks
WarioWare Touched!
Kirby Canvas Curse
Prof. Layton and the Unwound Future

1. Mario Kart DS - It's good to see a good series take such a leap forward into complete awesome. This was when Nintendo's limited online was far more acceptable so there's that, and also just a ton of great new content, new additions of missions, double the tracks using older games, multiple vehicles, and while the new tracks weren't all original (the ones that were original for Mario Kart were almost all references to other Mario titles), they played just as well as almost any other Mario Kart. Also, it's 12203 times better than that other handheld Mario Kart.
2. Pokemon: SoulSilver/HeartGold: Remake the best Pokemon games ever, update them with everything great from 4th gen (and all the Pokemon that existed before B/W) and fix anything wrong with the original versions. Even give the players the option to eventually go back to 8 bit music for even songs that WERE NEVER IN THE ORIGINAL GAMES. Even add things never used in a previous Pokemon game. I regret not playing it more than I have, and I played it for like 120 hours or something. I wish I finally caught them all (or at least close). But since I've lost interest with 5th gen, if I don't ever play a new Pokemon game again, I at least played this awesome game.
3. The first 4 Ace Attorney games. This is cheating, I don't care. I don't think on an internet forum I need to describe why these games are awesome. Great writing, awesome over the top characters, some of the most well done and defendable changes in the translation of a japanese game and just complete fun from genres both gameplay and story-wise I thought I would never get into.
4. Rhythm Heaven: This is simple really. Take Warioware, make it a rhythm game. Awesome idea that is somehow even better in execution. It is frustrating but so addicting you HAVE to keep playing, which I consider to be a sign (the sign?) of a truly great, difficult game (or maybe I just suck at Rhythm games, I dunno).
5. Chrono Trigger: Honestly, this should probably be 2nd, maybe even 1st, but it still has some minor things that kinda annoy me at times, but yeah. It's Chrono Trigger, the legendary RPG and one of the only SNES RPGs that is likely still as good now as it was back then (I say likely as I never had an SNES).
6. Advance Wars: Dual Strike: This is the 3rd game I have on here that's a genre I'm not exactly a huge fan of (or wasn't a huge fan of in the case of Ace Attorney). Maybe I should get into these games more, but than I'd have even more games to buy. Anyway, Advance Wars was a really good strategy game. Advance Wars 2 was a great strategy game with an insane amount of content for a GBA game. Advance Wars DS is a great strategy game with some of the best use of DS' gimmicks and somehow even more content. Incredibly addicting, fun and still better than Fire Emblem.
7. Radiant Historia: Yes, this should already be on the list. One of the best JRPGs of the best decade, often compared to Chrono Trigger and has tons of memorable characters, thanks to the brilliant White Chronicle time traveling and the many sidequests you will want to complete for many reasons.
8. Retro Game Challenge: 8 bit games. 8 of them in one game. Basically all of which would be worthwhile titles on the NES (or VC NES). Surprisingly awesome even if you're already expecting great retro fun. I still demand the sequel be translated!
9. Mario and Luigi: Bowser's Inside Story: After an "ok" Partners in Time, I am glad at how clever this game was. Half of the time it played very differently than the other two games, which was needed. The game was one big love letter to Bowser. Hell, Fawful was kinda dissappointing humor-wise, not to mention the weak final boss. But every single thing Bowser did was awesome, he stole the show and showed that this old villian deserves all the popularity he has. Especially, the giant Bowser stuff. Which reminded me of Dragon Quest: Rocket Slime. Which I only mention as this isn't top 11 DS games.
10. Kirby Superstar Ultra: I honestly played Canvas Curse more but Superstar is legendary. I mean, I think the main reason it exists is because they couldn't think of anything to make a full game out of so they made a bunch of shorter games, but that's ok, as they are all awesome. It also makes me think of Sonic Mega Collection and similar games. The first game IS basically Dreamland and the 2nd is somewhat similar to Adventure with the map, Gourmet Race is like an example of a side racing game for a series like Mario or Sonic (and eventually Kirby too), then a Metroidvania like game, then a game with a story and finally an arguably more basic game but with a complete change with how copy powers.work, which all seem like would be a natural evolution of many game series (much like how Castlevania changed after SotN, or how games often have more story nowadays, or how they change how major game mechanics work that no one would think ever change). But I'm probably thinking way too much into this.

1. New Super Mario Bros DS
2. Zelda: Phantom Hourglass
3. Kirby Canvas Curse
4. Mega Man Zero Collection
5. Contra 4
6. WarioWare: Touched!
7. Elite Beat Agents
8. Kirby Supr Star Ultra
9. Pac-Pix!
10. Castlevania: Dawn of Sorrow

Still need to play my copy of Animal Crossing: Wild World, not to mention I've got MM Zero 2-4 to play.
And then I also have 14 DS titles that a I need to snag to complete my shnazzy DS collection. And it still annoys me that we never got a classic styled proper Castlevania game for the DS...I don't think i could mange 3 Metroidvania games in a row.

Ten of my favorite DS games in no particular order:
Radiant Historia
Etrian Odyssey III: The Drowned City
Nine Hours Nine Persons Nine Doors
DragonQuest V: Hand of the Heavenly Bride
Might and Magic: Clash of Heroes
Castlevania: Dawn of Sorrow/Portrait of Ruin/Order of Ecclesia(can't decide, I love all three)
Contra 4
Maestro: Jump in Music
Mystery Dungeon: Shiren the Wanderer
DragonQuest: Rocket Slime

Pokemon Black and White
Ouendan 2
Legend of Zelda: Spirit Tracks
Super Scribblenauts
Kirby Super Star Ultra
Dragon Quest 9
Zelda Spirit Tracks
WarioWare Touched!
Kirby Canvas Curse
Super Mario 64 DS

1. Metroid Prime Hunters
2. Animal Crossing Wild World
3. Mario Kart DS
Super Mario 64 DS
Chibi-Robo Park Patrol
Pokemon Black
Legend of Zelda Phantom Hourglass
New Super Mario Brothers
Moon
WarioWare Touched

Too many great games on the DS to make a top 10 list that's concrete. I could easily put in Sonic Rush, Bowser's Inside Story, LoZ Spirit Tracks, Super Scribblenauts, Meteos, Star Fox Command, Pac-Pix, Custom Robo Arena and Tetris DS up there, and I'm still dealing with the likes of Kirby Mass Attack and Aliens Infestation. There's still a handful of DS games I still want to pickup. First system I've actually had a sizable log of games I want from years back.

1: Animal Crossing Wild World
2: New Super Mario Bros.
3: Kirby Squeak Squad
4: Castlevania Dawn of Sorrow
5: Pokemon Platinum
6: Legend of Zelda Phantom Hourglass
7: Chrono Trigger
8: Super Mario 64 DS
9: Metroid Prime Hunters
10: Tetris DS

I don't like most of the DS games I have that much. Such a dissapointing handheld. But here are the ones I like most:

New Super Mario Bros ( yes. Laughably easy, but still fun on the go. Love the Multiplayer )
Jump SuperStars ( essentially a portable Smash Bros, but with a Shonen Jump Skin.)
Kirby Superstar Ultra
Pokemon Black
WarioWare Touched
Mario & Luigi: Bowser's Inside Story ( Favorite Mario Character gets a starring role? You bet I'm gonna love it. )

...The rest were all pretty bad, even for handheld games.
I think I was dissapointed by the DS the most for the fact that it lead with Super Mario 64 DS, so I thought there would be lots of games with quality equal to the N64. They couldn't even make a good Zelda for this thing.

1) New Super Mario Bros.
2) Wario Ware Touched!
3) Mario Kart DS
4) Animal Crossing: Wild World
5) Mr Driller: Drill Spirits
6) Pac-Pix
7) Pokemon Diamond/Pearl
8) Mario vs Donkey Kong: March of the Minis
9) Phoenix Wright: Ace Attorney
10) Meteos

Though there are still a couple of DS games on my list to get, so they may have made the top 10 (had I played them earlier...)

only have few mario 1 and 2 6 golden coins...

1. The world ends with you
2. Super Mario 64 DS
3. Professor Layton and the lost future
4. Animal crossing: wild world
5. New super Mario bros.
6. Professor Layton and Pandora's box
7. Phoenix Wright: ace attorney
8. Professor Layton and the curious village
9. Mario kart DS
10. Sonic rush