1. Super Smash Bros. Melee ; Not just the best game Nintendo ever made, the best game ever made, period. An absolute masterpiece in every sense. Fun casually and competitively, the game has an unlimited movement system that gives you full control of a character and allows you to do whatever you want. There's no other game with freedom like Super Smash Bros. Melee, there's no other game with movement like Super Smash Bros. Melee, there's no other game that's hype like Super Smash Bros. Melee. There's a lot of content here, stuff that can entertain a kid in the early 2000s for dozens of hours as well. Whether playing with friends on FFA Temple as Roy, Samus, and Bowser, or competitively with Marth vs. Fox on Battlefield, the game is perfection. Bless the competitive scene for continuing to keep it alive.
2. The Legend of Zelda: Twilight Princess ; In 1998, when every other developer was still figuring out how the hell to make a 3D action game work, Nintendo came in and somehow perfected it with Ocarina of Time. They delivered in a way that no other developer could at the time, with masterfully designed dungeons, an engaging overworld, one of the best soundtracks in gaming, and controls/camera that actually functioned well. Twilight Princess is basically what Ocarina of Time would have been like if it was released in 2006 and if the developers said "What if we made this game twice as long?". The result is an epic, unabridged adventure that happily plods along at its own slow pace, and every bit of it is as memorable and well designed as OoT, with some of the best dungeons in the series.
3. Pokemon Platinum ; After some deliberation, I came to the conclusion that this is my favorite in the series. The Pokemon games are fantastic, mostly because of their battle system, which allows for much more depth than what is typically seen in a standard turn-based RPG, giving the player infinite freedom to create their own team. Gen 4 introduced online to the series and the physical/special split, and as a result a lot of the pre-gen 4 games feel a little wonky in comparison. Additionally gen 4 still has easily my favorite post-game content in the series, with the best and most fun Battle Frontier and a lot to do after beating the Elite 4. The others in the series are all hard not to pick, but they all have some sort of Fatal flaw. HG/SS has significant level unbalance, B/W1 is too linear and the new Pokemon are kind of shit, B/W2 is still linear and sort of ruins the great story of B/W1, X/Y feels kind of unfinished, and ORAS deviated from R/S/E too much with the designs of the new towns and no returning Battle Frontier. Platinum felt like it just gave us everything I wanted in a Pokemon game, and significantly fixed the issues on D/P's speed and Pokemon variety.
4. Fire Emblem ; The first released in the US is still the best in the series. The map designs here are absolute perfection, the story is solidly, it's really really fun to replay, and eases new players into the series well while still managing to be pretty damn challenging.
5. Mario Kart DS ; Sort of the Melee of the series in that it gave players a ton of freedom with their movement in a way the series never will again. The tracks are easily the best in the series. The inclusion of Mission mode made every other game in the series seem low on content in comparison. Just the perfect game to pick up and play at any time as well.
6. Elite Beat Agents ; When people use the word "charm," in reference to a video game this is what I think of. No other game has the heart and soul of Elite Beat Agents, with a story that manages to be corny, funny, and moving all the same. Playing through this game for the first time takes you on a whirlwind of emotions that you can't really recapture elsewhere. As a rhythm game fanatic there's not a ton of depth or content here, but somehow I still replayed the shit out of this game, trying to perfect my scores, because...well, I don't know, because it just has that heart and soul I guess.
7. Kirby's Adventure ; Pushed the NES to its damn limits. I admit this one might be largely in part due to nostalgia since I played through this game like 395033484 times as a kid or something, and the modern Kirby games are enjoyable but don't do much for me despite following basically the exact same formula. The amount of abilities make the game super replayable and the difficulty makes it something anyone can enjoy. Really responsive controls as far as the NES goes and maybe one of my favorite soundtracks on the console as well.
8. Super Mario World ; To this day still the best 2D Mario. The freedom and secrets here were tons and tons of fun to discover as a kid. Not the most balanced in the series but the most fun. Typical fantastic level design from the Mario team, but World is honestly one of the "weirder," games in the series in terms of enemies and locations, which makes the game feel fresh and stand out in the lineup of Mario games to this day.
9. Super Mario Galaxy ; SMG is like....Michael Jackson's 80s discography or something. It's just so effortlessly perfect and recognized as such by seemingly everyone that you don't even really know what more to say about it. While it's not my favorite Nintendo game, as made obvious by its number 9 placement on this list, it is basically everything great about Nintendo distilled into one game, with masterful level design, boss battles, level variety....everything. If someone asked me why I thought Nintendo was great I'd tell them to play Super Mario Galaxy.
10. Paper Mario: the Thousand Year Door ; Who would have thought that one of the best JRPGs of all-time is a Mario game on the Gamecube? tTYD is a reminder of a time from when Nintendo wasn't afraid to experiment with the Mario series. The result is some of the tightest writing in gaming and some of the most unique and varied locales in an RPG. The battle system is basically a tuned of version of PM64's, which is to say that it's pretty solid, and the badge system gives the player a lot of freedom. But the story and characters are really what bring it together and make it so memorable.
Decided to put a one-per-series (not franchise) limit on myself, otherwise the list would probably mostly be Pokemon.