Dragon Quest IX is the one game I have found that has literally infinite replay value. If you're a fan of RPGs, I highly recommend it. It's a bit pricey, but if you are fond of RPGs, go for it.
As for other DS games I can suggest? I'll say ones that haven't already been said. (Of those that have been said, Bowser's Inside Story and TWEWY are amazing.)
~Golden Sun: Dark Dawn - Probably one of the most vibrant and fun RPG games ever made. If you have played either of the first two you'll realize how much of a gem this is. The only real problems with it are there are points of no return (I believe there are a total of 3), so at times it isn't possible to go back and collect the goodies - and, when compared to the first two, the game is really easy. Nevertheless, I recommend it because...heck, it's Golden Sun.
~Ace Attorney series - There are 5 of these games, and they have both hilarious situations and characters as well as some of the most intricate plotlines you will ever see. (TWEWY has a great plotline, but even Ace Attorney can outdo them at points.) Oh, and the characters are pretty lovable as well. You basically play as a defense lawyer (Phoenix Wright in the first three titles, Apollo Justice in the fourth) who is trying to get your client acquitted, via a series of investigations and epic hijinks. The fifth game is a spinoff but works much the same way. They're relatively inexpensive, and the first one, which can be found for only $13 used at Gamestop, is probably the second-best in the entire series. And although the games are a bit short, you can replay it as much as you want, so it never really gets old. (I own and have played through all of them, and am currently in the process of replaying all the titles again - and it's just as awesome.)
~Mario Party DS *shot* Well technically, it's a lot like Mario Kart DS - it's great as a single-player game, but the play value practically triples if you have a bunch of friends you can play it with. And the multiplayer is single-card (DS Download Play), so if you alone have it you can play with up to 4 people. Good party game.