I have elsewhere put together a list of recommended DS games so I will share that here ok (it is long sorry)
games with asterisks around them are the best of the crop IMO
some of the descriptions are made assuming you know something about the game's quality already (example: castlevania) without needing to be told
Action/Adventure:*The Legend of Zelda: Phantom Hourglass*
This was a great game !!! The controls take a bit of getting used to but after playing for a bit they are cool
*Castlevania: Dawn of Sorrow* (lol castlevania)
*Castlevania: Portrait of Ruin* (lol more castlevania)
*Lunar Knights* (Part of the Boktai line of games, but there's no solar sensor - an in-game day/night cycle and controllable climate system replaced it. This game has amazing production values and stuff though and is fun !!!)
Metroid Prime: Hunters (added by Garvar)
If you like Metroid Prime, there is really no reason to not check this game out. Unless you don't have a thumbstrap for your DS, because the thumbstrap control is what made this game so enjoyable and easy to play for me. It's a fairly lengthly game the first time through (granted when I got to near the end of the game I spent two or three hours figuring out where to go do a 5 to 10 minute task) and the bosses are often repititions of previous bosses, but it is quite a well done game and the only good shooter on the DS I'm aware of. Also thanks to the touch screen, shooters can actually belong somewhere other than the PC now.
Starfox Command (added by Garvar)
I would recommend Starfox Command because I have been having lots of fun with it ever since I mastered the controls but I think I'm the only one who likes it.
New Super Mario Bros. (I mostly just played the multi player part of this game (with my brother) which is very entertaining, especially if you are playing it somewhere that you can yell obscenities at each other. Unfortunately, it is not wifi enabled oh my god my girlfriend left me I am going to cut myself)
RPGs:*The World Ends With You*
Probably my favorite DS game next to EBA, this unique RPG has a cool story is fantastically polished. I can't say much without spoiling stuff but this is definitely worth playing !!!!!!!!!!
*Pokemon Diamond/Pearl*
It's pokemon
*Custom Robo Arena*
(The battles have a fair amount of button mashing but it is fun. This game also has some lol)
*Mega Man Star Force*
This is supposedly pretty similar to the Battle Network games, so if you're expecting something completely new, you might be disappointed. I never played the BN games though so I didn't have that problem :[!
Mega Man Star Force 2
Not very far into this one so idk
Final Fantasy Fables: Chocobo Tales
(this is a pretty ^_^esque game, and while some of the mini/micro games are pretty dumb, the "pop-up duels" are pretty fun)
Final Fantasy III
(This is a good time sink if you like old-style RPGs with simple stories and stuff, plus there is a lot of class customization available as you get each of the 4 crystals)
*Etrian Odyssey*
This game is punishing and is not for everyone - it's an old-school style rpg in which you draw a map on the bottom screen (mainly walls, doors, etc). It's a great game if you can take the beatings.
*Etrian Odyseey 2*
Some nice improvements over EO1, making a great game even better !!!
Magical Starsign
(From the makers of the ____ of Mana games iirc, this is a pretty fun game with some lols, it uses the touch screen for pretty much all of the controls, which I usually don't like, but it worked)
Contact
(I haven't played this one much yet, but it seems neat)
Strategy / SRPG:*Final Fantasy Tactics A2*
(duh it is FFTA2)
*Luminous Arc*
Published by Atlus, which is reason alone to look into this game. This is the first non-PC SRPG that I know of that has online battling, which is cool - you also get items for doing so, whether you win or lose. The game itself is also fun, and it has quite a lot of voice acting, which adds to the immersion (LOL!!!!!!!!!!).
*Advance Wars: Dual Strike*
(I only recently started it but Advance Wars games are good ok)
Izuna: Legend of the Unemployed Ninja
(oh wait this isn't a strategy game :[ this is a pretty short game but it is fun while it lasts also it is lol)
Pokemon Mystery Dungeon
(I might as well keep putting these roguelikes in strategy I guess lol
I started this game and it seemed cool enough, but I didn't really get into it.)
Racing:*Mario Kart DS*
(there are not many DS racing games that are noteworthy but Mario Kart is fun)
Diddy Kong Racing
(actually this isn't that great - the N64 version was much better)
Puzzles:*Picross*
wow I've played this so much - it's comparable to sudoku, but it's too unique to be called similar to it. You're given numbers on the left and upper sides and you have to figure out which squares get filled in and which ones don't, and the end result is a picture. It also has wifi, with which you can download/exchange puzzles or play against people
*Planet Puzzle League*
(Similar to Tetris Attack - has wifi multiplayer)
*Meteos*
(Easy to pick up and play, this is a fun game !!! also the Luna = Luna planet rules lol)
Puzzle Quest - Challenge of the Warlords
(RPG puzzle game with some lol dialog, I haven't finished this one yet though ok)
Tetris DS
(who doesn't like tetris seriously
)
Honeycomb Beat
(this is cool but hard to describe)
Sports:True Swing Golf (added by Garvar)
I never really cared a whole lot for golf games other than the GBC Mario Golf but this game is a lot of fun and incorporates touch-screen play very well. The graphics are pretty awesome and there is a neat "campaign/career" mode where you get to create and customize a character with all sorts of crazy golfing antics and whatnot. But really it's just a fun golf game. EDIT: If any of the DS games I played at work were to get me fired, it'd be this one. For anyone who actually golfs, this game can really capture you. A few times I was sitting in my cubicle, I nearly jumped out of my chair with a fist in the air because of an awesome pin shot or a 65 foot putt that miraculously found its way into the hole.
Clubhouse Games
(I have barely played this but it has wifi and lots of games to play. Added this to sports because it has bowling !!!!)
Rhythm-based Action Games:*Elite Beat Agents // Osu! Tatakae! Ouendan! // Ouendan 2* (because they deserve their own section lol)
Other:Rune Factory: A Fantasy Harvest Moon (harvest moon + dungeon crawler + graphical overhaul = cool game)
*Phoenix Wright: Ace Attorney // Phoenix Wright: Justice for All // Phoenix Wright: Trials and Tribulations // Apollo Justice* (Addicting games, great stories, high quality !!!)
Animal Crossing: Wild World (this is pretty fun, but I am not really fond of real-time based games in which weeds mess up beautiful Aiur in my absence
! )
Brain Age 1 and 2 (this is a neat game and it has sudoku which gives it a big plus ok)
Trauma Center: Under the Knife
This is supposedly "one of those games that makes the system worth owning" but I never really got into it.
Lost In Blue 1 // 2 (added by Garvar)
The Survival Kids games were pretty neat and Lost In Blue, though it has little to no replay value, is an interesting game. You're stranded on an island and have to survive on, essentially, nothing (at first). You can dig for shit, shaking trees is good if you find something to eat in them or something to make a weapon out of. The only real qualm with this is that there are essentially two or three "headquarters" you can inhabit where you can cook meals and make furniture in and shit like that. Also it gets pretty confusing later on in the game when you start to explore the island more.
Feel The Magic (Minigame game) (added by Garvar)
This is the first DS game I bought, and I think it was a launch title from Sega. It's got a quirky nature to it and is quite charming. The only problem with it is that it's insufferably short. A lot of fun, but only for a little while. There's like 12 minigames, and they each take about two minutes each once you've mastered them, and up to about 10 otherwise. You're looking at maybe 5 to 10 hours of enjoyment out of this, total.