Oh, these favorite lists are always enjoyable to do! Let me contribute a little something. . .
#1 - Super Mario RPG: Legend of the Seven Stars
This I would say is definitively my favorite Mario game to date. As a fan of J-RPG's (and the old SquareSoft team), collaborating with Nintendo to create a turn-based game influenced from the classic Final Fantasy titles ended up being in my opinion, an ingenious blend. Having strayed away from the typical "Princess is captured by Bowser" story, this game allowed me to experience characters such as Mario, Toadstool (better known now as Peach) and Bowser in combat together for the first time. As if that weren't enough, original characters and enemies such as Mallow, Geno, Booster (etc.) were very much likeable, and became some of my (and many others') personal favorites. Boss characters were all original and diverse, each posing different and entertaining personalities. While the game wasn't particularly long compared to other RPG's, I never considered that to be a flaw as I find myself replaying through the game from time to time (I've at least completed the game around 15 times). The soundtrack is exceptional, providing some instant classics (the most infamous being "Beware the Forest Mushrooms"), and I felt the themes and area's of the game were very fitting. SquareSoft even took it a step further to add a fairly difficult optional boss that goes by the name of "Culex", who spots the Final Fantasy IV boss theme when you battle him! If I had to take away anything from this game, it would be that Luigi lacked an appearance, and that there hasn't yet been a proper sequel to it!
#2 - Super Mario World and Super Mario Galaxy
Respectively, I am putting these both as second on my list, rather than choosing between two and three for the purposes of a side-scrolling platformer as opposed to a 3D platformer.
Super Mario World for me admittedly has nostalgic value, as it is one of the first games that I have ever played, and is the first game that I had ever beaten on my own (at 5 years old, mind you!). I still feel that to this day, there has yet to be a side-scrolling Mario game that matches what this game had accomplished in level design, visual appeal, music, etc. The levels feel so much more involved than the recent New Super Mario Bros. series (which I believe needs to be dropped, but that's a discussion for elsewhere. . .), from the enemy involvement to the layouts of the levels themselves, and although they are both Mario games, Super Mario World to me feels like it is one that has a more "serious" feeling to it. Basically, I still find it to be the pinnacle of the side-scrolling Mario series, and if Nintendo plans to continue the side-scrolling Mario series, I would hope they reboot it with something original that has more effort put into it soon.
Super Mario Galaxy. . . Now this game was something else. My 3D Mario platformer of choice, it was one of the few titles that had the ability to toss away the visual deficiencies of the Wii to really showcase a gorgeous game. The animations are smooth, the colors were vibrant, and the soundtrack was the first orchestral take on the Mario franchise as a whole (I know I'm not the only one who wasn't expecting that final Bowser theme at the end!). I recall some fearing the levels could become stagnant pre-release, but those fears were put to rest. The level design is quite magnificent and plentiful, having different galaxies / planets to travel to for diversity, and with 120 stars in total to be collected, you would be able to unlock the Super Luigi Galaxy mode as something extra. It wouldn't be Mario without power-ups, adding some new instant classics such as the Bee suit (one of my personal favorites). Mario Galaxy 2 expanded upon the first (and one can argue is superior in every way), adding a larger amount of levels and additions such as Yoshi, but having played through Mario Galaxy first, it left more of an impact than the sequel had for me (it sort of felt like an expansion that could have been DLC today). I do hope that the next 3D Mario platformer strays away from the Mario Galaxy series, and at the same time could reinvent itself into something that is just as extraordinary.
Honorable mentions - Paper Mario: The Thousand Year Door and the Mario Kart series
Paper Mario: The Thousand Year Door is an excellent title. Expanding upon the original Paper Mario for N64 (also a game I thoroughly enjoyed), it was a recipe for success. Delving the Mario characters once again into RPG territory, the story is satisfying and fair in length. Many characters, playable and not, are ones that are original and unique (Rawk Hawk was quite memorable, ha ha), and overall, the game just did things the way it should have. Its successor, Super Paper Mario on the Wii, while having an interesting story, abandoned the traditional turn-based style gameplay, something the majority of people have been against, and Paper Mario: Sticker Star on the 3DS just didn't do the series justice (I personally didn't even purchase it). If they plan to continue this series, hopefully they can bring it back to its turn-based roots while expanding upon new features from there (perhaps a bigger overworld, etc.). I know it's Paper Mario, but it wouldnt hurt to see it be taken a little more seriously. . . Seeing it in HD on the Wii U would be pleasant too, assuming that the GamePad could potentially be utilized for some pretty unique options within the game.
For the Mario Kart series, I'll keep it short and sweet. The games are loads of fun, whether by yourself, or even moreso when playing with other people (online or locally). I know that come around the launch of Mario Kart 8, similar to what we'll do for SSB4, a few of my friends and I are going to get together, order up on some pizza and soda and just have a good time playing. That being said, I strongly believe Mario Kart 8 will be the best in the series, if not my personal favorite, at least.
Things to take note of:
I do not yet currently own a Wii U, and so I haven't any experience with Super Mario 3D World (though I've of course heard of how excellent it is, in particular of how fun it can be). I do however plan to pick one up around the launch of Mario Kart 8, though it may have to wait a week or two after due to money constraints. . . Anyways, that's my list! Whether you tend to agree or disagree, I do hope my opinions were enjoyable enough for everyone.