Just because I'm bored, I'm going to explain my choices:
1. Super Mario RPG: You probably don't realize how much of a game changer this was unless you grew up with it. This was the game that pretty much proved that Mario could do anything and it was very exciting to think of what the future could hold. It had a great cast of characters, great humor, an absolutely legendary soundtrack, and a ton of content for a Mario game.This was the definitive game of my childhood.
2. Super Mario Galaxy 2: I loved Galaxy but I also thought it was too easy. To me at least, I feel that this was the game where Nintendo noticed that most people thought most modern Nintendo games were too easy and actually started to do something about it. It took everything that was awesome about Galaxy and doubled it and I would argue that there was as big of an improvement between Galaxy and Galaxy 2 as there was between Banjo Kazooie and Banjo Tooie.
3. Super Mario Bros 3: Another game changer because it went back to the basic formula of the original games and greatly expanded upon it. Tons of levels, tons of power ups, tons of secrets, and enough difficulty that it could be hard at times but not enough to throw your controller across the room and through a wall. Definitely a classic and a prime example of how to properly do a sequel.
4. Mario and Luigi: Super Star Saga: This was probably one of the first games I ever played that literally made me laugh out loud whether it was from the antics of the characters or just the off the wall dialogue peppered through out the game. Fawful and Prince Peasley not becoming staple characters in the franchise is almost as big of a crime as Geno and Mallow not either as far as I'm concerned.
5. Super Mario 64: I'll admit, this game has aged horrifically and is downright ugly to look at now-a-days but back when I was 9 years old when it first game out, it was explosively crap your pants exciting. Mario? IN 3D?! JESUS OLD MAN RIVER TAP DANCING CHRIST, THIS IS THE BEST THING EVER!!! My parents literally had to carry me away from my friend's N64 the first time I played this game and there's just so many great memories tied to it. Going down the slide for the first time on Cool Cool Mountain... using the wing cap for the first time... zoning out while listening to the music in Jolly Roger Bay... throwing Bowser face first into a bomb for the first time... There's so many great memories tied to this game that wouldn't be topped for me until years later with Super Mario Galaxy.