Lemme open up my own DS case and recommend some games.
Big Brain Academy: Stated before. A good game for wasting some moments, but best played in short bursts. The little exercises for your brain can get kind of draining after a while. The “ooh thinking so much” kind. Still, it’s fun and addicting to keep coming back to.
Puzzle Quest: mentioned before too. If you like Bejeweled and a little D&D thrown in, then this is a game for you. Addicting, and it’s the kind you can play for minutes or hours at a time. I have it for my PC and my DS. There are a few bugs in the DS version, but nothing that makes it unplayable.
MarioKart DS: Also has Wi-Fi play over the internet. Fun racing game with popular Mario characters, a definite must for multiple DSes in the house.
Animal Crossing Wild World: The game is basically a little village in which you live. That’s about it. You can grow fruit trees, talk to people, pay off your house, fish, find little things buried…overall, not too thrilling when playing by yourself, but friends can visit others’ towns by sharing friend codes. Also Wi-Fi enabled for internet play, and if your kids get it, you can visit each others’ towns.
Zelda - Phantom Hourglass: Heavy use on the stylus in this game. Also enabled for Wi-Fi as well as play with others nearby, though the multiplayer is a fun little game where you collect Triforce parts for points while your opponent guides three knights to try and slash you and end your turn. Though the fact you have to keep returning to a certain temple to keep the game going gets repetitive, especially since you have to do floors over and over again.
Elite Beat Agents: Mentioned before as well, quite fun, varying difficulties can be chosen. Allows for multiplayer by allowing you to face off against a friend in songs. The final level is quite hard. As in, “can bring grown men to tears” hard. 
Lost Magic: A quite basic RPG that plays a little like the old Warcraft, where you can guide your units with your stylus and tell them where to go or attack. The fun point is being able to draw runes on your touchscreen with your stylus to activate your spells. Also Wi-Fi Enabled.
Heroes of Mana: Even moreso like the old Warcraft games, as you have to not only guide units all over large maps, but also harvest raw materials to build things while in-battle. Wi-Fi enabled I think, haven’t played mine much.
Cooking Mama: “Bettah zen mama!” Play little cooking minigames to complete your dishes. Peel, chop, slice, dice, stew, saute…learn styles of cooking while having fun. I like it, I recommend it. Though peeling carrots seems so hard…
Nintendogs: Mentioned before, you can also visit other DS owners’ dogs by enabling “Bark Mode”. This can unlock new items and breeds. By using the microphone in your DS, you can communicate to your dogs by calling them over by name, and issuing commands like “Sit!” and “Roll over!”. Very fun for a while, and the cuteness can reel you in, but since you need to really care for them daily, it can get kind of old. I haven’t seen my puppy for months. He’s covered in fleas by now I’m sure. Though…don’t do it in public places other than at home, people will think you’re crazy. 
Luminous Arc: A very good RPG game not unlike Tactics Ogre or Final Fantasy Tactics, where battles are done on a grid-like battlefield. Has good humor that doesn’t take itself too seriously, and the voice acting is very good. I highly recommend it if you like roleplaying games. Although battles can take a while.
Trauma Center - Under the Knife: Become a surgeon! Use your stylus as a scalpel, a medical laser, a syringe, and other tools. Better classified as a Puzzle-type game, it isn’t gross in terms of blood or anything. I very highly recommend Trauma Center, as it’s quite unique and easily reels you in. The surgeries are all on a timer and usually aren’t any longer than five minutes at most, and you can always replay them for higher scores.
Rune Factory: Also Wi-Fi Enabled. You’ve been given a farm and land on which to grow your crops, but the caves nearby are also hiding secrets. Clear your land of debris and grow your crops according to season to earn money, as well as raise monsters for milk, honey, and eggs. While caring for your farm and interacting with villagers, explore the mysteries of the different dungeons nearby. Using raw materials, you can also craft items, forge tools and equipment, cook in your kitchen…plenty to do. Highly recommended.
Castlevania - Portrait of Ruin: Also Wi-Fi enabled. Explore a large castle while switching between two characters, each with their own style of play. Along the way, explore worlds hidden inside of large paintings to eventually take down the vampire who rules this castle. A variety of weapons and magic spells allows you to find your own style of play as well. After beating the game, you can play it again as different whole new characters too. I recommend this game as well.
Metroid Prime Hunters: Mentioned earlier, also Wi-Fi enabled. The controls can be a little tricky to get down, and if you have large hands, the way you have to hold the DS Lite can make your hand ache after a while; at least, it does for me. Despite this, it’s a very good FPS-style game that can offer a really good challenge. I recommend it, but I haven’t played mine much.
Phoenix Wright - Ace Attorney: If you don’t get this game, it’s practically a sin. j/k
Although you can use vocal commands for the game, (and you should when you’re able to and not completely in public, it makes it so much more fun), you don’t have to. As a rookie attorney, you’re constantly thrown into some complicated cases where nothing is as it seems. Investigate and gather evidence, then with your knowledge and evidence, press your witnesses in court. Catch them in their lies, uncover the truth, but be careful: mess up too many times in court and you’ll get an instant game-over. Start with the first in the series, and if you like it, check on the others. Plus some characters you can’t help but love, or love to hate.
EDIT: Oh yeah, and if you want to really make your DS stand out, check out these awesome skins you can buy for it. I bought the aloha black skin. I love it, makes it really stand out when you have a white DS with aloha print. 