I can't believe Bust-a-Move gets so many votes. I mean, I think the whole series is sort of mediocre, but the Neo Poke version is sub-par even at that. There's just no challenge to it. The best thing is the puzzle mode, but even that is still kind of piddly; Puzzle Link 1 or 2's puzzle mode is much better.
Picture Puzzle is cool, too, or rather the game it's based on is cool. I don't think it makes such a hot video game, though. You're really better off just buying a book of those puzzles or printing them out from the Internet and doing them with pencil and paper.
My vote goes to Puzzle Link 2. Great game, not too furious like Magical Drop or too slow like Bust-a-Move, it's juuuuuuust right. And I find that the card collecting really makes it a lot more fun (even though the card battle game is lame), love the cutesy little quotes on the cards.
I suppose you're not counting homebrew, but I've got to say, my actual favorite puzzle game on the Neo Poke is Puzzle Gems by rtb7/Roger Dupond. It's basically the same as the Flash game Zookeeper, if you know that one. Excellent, excellent game. Probably the best puzzler since Tetris.
...word is bondage...