My favorites are admittedly fairly generic.
1. Pokemon Platinum. While I first started playing Pokemon with Fire Red and Leaf Green, I didn't get super into the series as a whole until Diamond and Pearl which I played extensively. Platinum still gives me that rush of nostalgia for Diamond, but fixes every problem I had with it and then some. I unfortunately lost my first copy, but I still had just as much fun starting over on a new copy. I picked up another one last year and it honestly still holds up just as well now as it did then, plus knowing more about the games and the series allowed me to have an even greater appreciation for the game this time through.
2. Heart Gold/Soul Silver. Johto is one of my favorite regions and I especially loved being able to go back to Kanto, so when the games were being remade I was ecstatic. I bought Heart Gold right at launch and spent way too much of my life with that game, so much so that the contacts actually started wearing out and the game often takes a few tries to read. This was pretty much everything that a remake was supposed to be, sticking close enough to the original that it's recognizable as such, yet acknowledging and implementing improvements brought by the third game in the generation, plus adding the changes and improvements of the current gen. And then, on top of all of that, they also added completely new features as well such as the Pokeathlon or the Safari Zone which was absent in the original Gen 2 games. Essentially, it's the exact opposite of what Brilliant Diamond/Shining Pearl were.
And now for something that isn't Pokemon:
3. Mario & Luigi: Bowser's Inside Story. I loved Superstar Saga, and when I came across this game sitting on a store shelf I had to have it. It does everything Superstar Saga did well and then more. I love how even the same game world becomes so different based on how you can interact with it, depending on whether you're using Mario and Luigi or Bowser, and the puzzles and floors inside Bowser are really well designed and a nice nod to the 2d Mario platformers. Great music too, especially that final boss song that goes way harder than it has any business doing and is incredible. I have Partners in Time but have never played it for some reason, maybe I should think about booting that up one of these days...
4. Pokemon Black and White. Surprise surprise, another Pokemon game makes the list. In my opinion the DS era was where the Pokemon series peaked. B/W are a shining example of this. While many disliked it, I loved that the game essentially acted as a sort of "soft reboot" of the series, limiting you to only Gen 5 Pokemon until after the Elite Four. It forced me to try out various Pokemon I'd have likely skipped for the more tried-and-true ones of previous gens, and I loved the designs of the vast majority of these Pokemon. I also loved how dynamic the game was, with routes and cities changing not only in visuals, but in accessible areas as well as the seasons changed each month. Even the music was incredibly dynamic, with songs that changed with the seasons, or depending on which NPCs you spoke to in an area (Village Bridge comes to mind here, but also Anville and Accumula town had this as well), or in some cases whether you were walking or running. I also can't forget the views and camera work the first time I crossed over the Skyarrow Bridge into Castelia City, and the music for that route is my second favorite overall in the whole series. It really felt like the developers poured their hearts and souls into this game, so it's a real shame they were received so poorly relative to the games before it.
5. Magician's Quest: Mysterious Times (that's the US title anyway). I bought this one for $6 at GameStop on recommendation from a user on another forum to tide me over in the wait for New Leaf and it was way better than I expected. It has a fair amount of similarities to Wild World such as the rolling log map, interior decoration, and "villagers" that move in and out periodically, but it goes significantly deeper than Wild World does in terms of villager interaction, shops, and just about every other aspect of the game. As you might have guessed by the name, the game does have a fairly strong focus around magic, with a very extensive spell book based around building magic phrases from a huge list of words (the in-game school the game is based around has classes most days to help guide you along) which can help you with quests or just daily life, but in the end you're really just free to live your life around the town like you would in Wild World. I would highly recommend trying this game, but unfortunately prices for this game have spiked in recent years so it might not be worth getting unless you can find a great price somewhere (at this point, even $40 would be a good deal).
Honorable Mentions:
Mario Kart DS. Not much to say here, it's a classic.
Animal Crossing: Wild World. Not the strongest in the series, but what it did it did well enough to be an enjoyable Animal Crossing experience, if not a bit barebones for Animal Crossing standards. It provided me with a couple years of near-daily (and weekly at the very least) Animal Crossing entertainment and I still check back in on it from time to time.
Guitar Hero: On Tour series. I was obsessed with Guitar Hero for a time, and these games were surprisingly good for what they had to work with. I did make the mistake of playing this on my first DS Lite without a screen protector, and it scratched the ever living crap out of the touch screen to the point where I was surprised it was even working at all. I've since learned my lesson. Unfortunately I don't play anywhere near as frequently as I used to, and as such am nowhere near as good as I used to be at it.
WarioWare: DIY. While I never was the best at making Microgames (I did have a couple I was fairly proud of though) and spent much of my time with the game maker just butchering the included microgames, I did have a lot of fun with the song maker and made quite a few fairly decent remakes of other video game songs. Every now and then I jump back into the music maker and churn out another song.