Can't really pick ONE, but....
Super Mario 64 is special to me because it was my first ever video game.
Otherwise, in terms of my favorite story, Super Paper Mario is my favorite. It gets a lot of criticism, and it's all warranted for the most part, even I hated this game when it first came out. But once I tried it again a few years later, I absolutely loved it despite its flaws. The villains are complex and interesting, the plot itself is the most serious I've ever seen a Mario game take itself- I mean, you don't just save Princess Peach or The Mushroom Kingdom- you have to save the entire freakin' UNIVERSE, which is filled with other worlds and dimensions that are all counting on you, or else everyone everywhere will DIE. I mean, if that's not hardcore enough, one of the levels in this game is LITERALLY hell. It's an amazing game, I really recommend giving it a try, especially if you previously disliked it for whatever gameplay reasonings you had, because the story and characters are worth it, and there's a phenomenal and touching ending scene.
For the RPG's, that's a little tougher to decide between, because Super Star Saga had a great setting and some great villain intros, but I feel like Bowser's Inside Story is great too, but for different reasons. The script is hilarious, for one, Bowser and Fawful's banter sessions are great, and just any opportunity to play as Bowser is fun in general. I really enjoyed the game for the most part.
Mario Kart Wii also holds a place in my heart, even though a lot of people might not have hailed this as their favorite kart game, but for me, it provided countless hours of relaxation after school. I enjoyed playing online regularly, the glitched matches were a lot of great fun, and really felt quite sad once the servers were shut down for it. But then I eventually got Mario Kart 8, so all was well with the world again.