If it's a Lite or just fat ds then you can use any flashcart, if it's a DSi or anything above buy a DSTWO.
There are really so many great games. It'd help if you listed types of games or genres you like (since you mentioned not liking Elite Beat Agents). My top: 999 (Incredible game, but make sure you play it again to earn the "true" ending.) Castlevania: Dawn of Sorrow Ghost Trick (Haven't finished this one yet). Pokémon: Soul Silver (or any of them really, but this one's my favorite.) Wario Ware: D.I.Y. (If you have any inclination to try making your own games/music. Samples Here: http://www.youtube.com/watch?v=EJhkio_vPE4&list=PLEFD060A445599C44) If you happened to grab a DSi, then I'd also add the DSiware games: Boxlife, Base 10, and Shantae: Risky's Revenge.
Anything with both the words "Ace" and "Attorney" on its title will make owning a DS worth it. The first Ace Attorney is the coolest one, because of the soundtrack and because of Maya and Ema. But you'll want to play the next three nonstop if you get the first one. Get all four Ace Attorney games. Worth every penny. Xerdo guarantees this.
My recommendations are: For platformer fans: Mario Spyro shadow legacy for RPG fans: The Urbz The Sims 2 For City building fans: Simcity Creator
Bangai-O Spirits is way too awesome to pass up. Probably one of my favorite games on the system hands down. This game is the sheer joy of destruction put into a DS cartridge, and then multiplied a thousand times by you being a mecha shooting missiles bigger than you at sometimes hundreds of enemies and bullets. Big great fun, with a ton of levels, a level editor and a competitive multiplayer mode to boot. Can't recommend this one enough. Then, in no particular order : - Rhythm Tengoku : perhaps one of the best rhythm games around, tons of fun. - Flower, Sun and Rain : a port of a Suda51 PS2 game, that's of course a bit lesser on the graphical side, but still the only way to play the game in english. It's a kind of cross between a point n'click adventure, a visual novel and lord knows what. It's very much in the line of other Grasshopper Manufacture titles. I won't spoil anything, but it's quite unique. - Contact : another Grasshopper title, this time a Mother-influenced RPG with interesting mechanics and a cool twist on the double-screen thing. - Etrian Odyssey : there are three of them, it's a series of punishingly hard Atlus RPGs (so, Atlus RPGs, in short). Very old school, not the kind of game where you get held by the hand. Quite entertaining if you're into that kind of thing. - Picross DS : really the same game as all the other iterations, but the DS interface makes it really intuitive, and it's the sort of thing I never get tired off, great way to kill time in public transportation and so forth.
I second Rhythm Tengoku as a very solid option. I will add to your list, obviously, New Super Mario, Super Robot Taisen OG Saga (RPG and lots of girly fanservice. Neat), the GameCenter CX games (the second one if you read Japanese, as it has no western release) and also Bokura no TV Game Kentei is very very enjoyable. Also the Rockman ZX games are very good. And if you can still find one, Space Invaders Extreme and Arkanoid are a joy to play with that special dial controller there was.
I didn't even know there was a Robot Taisen game that has been translated. I gotta see what the series represented in this one are, I love the RT games (well of course, I love mechas). And as a Megaman fan I have to find the ZX games too, but I've never been able to get my hands on them. Forgot Space Invaders Extreme. That one's way cool. Almost Rez-ish in it's approach of the shooting genre via the rhythm angle.
There are also two GBA Robot Taisen games localized in the US as well, but those (including the DS entry) are all "Original Generation", meaning no other IPs were used or licensed. That's how they got around it. Perhaps if the upcoming Project X Zone does well then that'll open the door a bit wider for more games of this nature.
That's what I gathered from reading the wikipedia entry. It's too bad, I was looking forward to an EVA vs Zeta duel in the pocket (like in SRTF) but I guess I'll have to keep playing the Japanese titles while skipping most (all) of the dialogue. Although I'll still try to get my hands on this one, I'm always up for a humorous RPG. I've played through Magical Starsign (on the DS too) and while it was mostly unintentional, it was indeed quite hilarious.
I am salivating for Project X Zone, continuously. The word "want" does not even begin to encompass a fraction of my desire for that game. It is sexy as fuck, and I require it with urgency.
Some of the games worth getting, include: Yoshi's island DS Super Mario 64 DS both of the Mario vs DK-games Magical Michael - Pang (Basically a modern version of Super Pang/ Super Buster Bros.)