Hmmm, strat and puzzle... Meteos, definitely. It's really absolutely great. I always think of Nanostray when I want a puzzle game ^^; ...but Polarium is actually a better one. Even better than Polarium, IMO, is Magnetica. Puzzle Quest is much better than I initially gave it credit for -- it's puzzle
lite in some ways but it's still a great title, esp with friends. Almost any multiplayer game for DS is really nice. DS Download Play is incredible. Mario Kart lets you play 8 players with one cartridge, iirc. Tetris DS is surprisingly good -- it includes more versions of Tetris than I've ever seen -- not counting the homebrew great, Lockjaw.
Strategy-side is much weaker. Don't buy into Advance Wars unless you want a rehash of the GBA titles. IMO, it's terribly overrated. However, if you loved the GBA titles (or haven't played them) then go for it. As a plug for the only strategy game worth the cartridge it's made on, Sangokushi is pretty good. It's Romance of the Three Kingdoms -- but not available in English (and being able to read it is pretty useful). RPG wise, things get much better. Daisenryaku is basically a refreshing take on Advance Wars with a more military theme (AW's main flaw IMO is a stunning lack of worthwhile new features), Japanese knowledge not really necessary. Tank Beat is a pretty nifty action tank game with innovative DS controls -- Japanese isn't necessary but an FAQ helps!
I love RPGs so I know the most about this -- Lost in Blue 1 & 2 are basically living classics -- possibly the best new games of this console generation. Izuna is a fantastic roguelike, but not the greatest portable game, because if you quit, you lose (almost) all your stuff. However, DS suspend mode is amazing. I've left it on suspend for 16 hours before --
after getting a low battery warning! Mario & Luigi Lost in Time is pretty close to perfect (prob depends on how much you liked the Paper Mario series). Pokemon Rangers and Pokemon Pearl are both surprisingly good. Harvest Moon DS is great. Animal Crossing is another game that's great if you didn't already play it for the NGC.
On to other categories, things get
much better... Phoenix Wright, Trauma Center, Wario Ware, Nintendogs (caveat: it is JUST a virtual pet!) and Cooking Mama are all that they're cracked up to be. Hotel Dusk is not, unless you have that patience needed for classically bad adventure games (my g/f does..!). The Castlevanias are solid but basically identical to Symphony of Night (and every bit as good). Lesser known gems include Monster House, Bomberman Land Touch!, Point Blank, Tennis no Ouji-Sama, Kirby Canvas Crush and Power Paintbrush, Custom Robo, Brain Training and Big Brain Academy are pretty good, if you like that sort of thing -- basically puzzle games that track your performance, more on the mathy side of things than the gamey side of things.
All that said, we play Clubhouse Games more than any other DS title, probably two or three times as much -- it sounds dumb, and it is. It's a classically gimped version of a few dozen traditional card and board games -- they would leave you scratching your head if it weren't for multiplayer. DS Download Play makes Clubhouse Games the perfect game for any multiplayer situation, with young and old alike, no matter how much free time you have available. Although you likely will have played "better" (more flexible and better AI-ed) versions of almost all of the games included, it also includes the lesser-known Japanese classics, Shogi and Hanafuda.
Others Overrated (IMO, no need to flame!): Lunar Knights, Elite Beat Agents, Rub Rabbits...