My parents and older sisters played a lot of SMB3 on the NES (before the NES crapped out because one of the sisters put one too many sandwiches in it), and my mom and dad were pretty good at SMW, but I pretty much always just watched them rather than playing myself, until I got my own Game Boy for Christmas (from Montgomery Wards, at a going out of business sale), with Super Mario Land. I also got a Game Genie for it either at the same time or shortly thereafter. SML was the only game I ever owned that the book had any codes for, and I would always play it with Infinite Lives, Walk Through All Walls, and Always Big Mario. Oftentimes I would take the Game Boy into the bathroom and beat the whole game (with those codes) while on the toilet.
The Game Boy served as a bridge onto the SNES. My most-remembered games from there are SMW, SMAS, Plok, Lion King (I never got past the second level and that [darn] ostrich-jumping section), Tom and Jerry, Sim Earth (good music, though the intro with the eye logo and the sweeping planets usually scared me, and I would often wait a while to turn on the TV when playing it so as not to risk seeing the intro) and my favorite game at the time, Mario is Missing. I liked it because it had Luigi, you couldn't die (though the unloseable boss battles still felt intense), the music was nice, and Bowser had the right coloration rather than having green arms and orange palms like in SMW. And the part at the end where Bowser gets launched into the snow and freezes solid and shatters to pieces was pretty badass.
One day while my mom and I were at the rental store about to rent Mario is Missing again, we saw Mario RPG. We both became rather obsessed with the game, and soon bought our own copy. She beat it before I did, but I still played the hell out of it, and made my own continuations of the story with my little brother's toys. A Little Tykes bus driver with red pants and a blue hat was Mario, a white Snoopy-esque Little Tykes dog was Mallow, one with a blue shirt and brown hair was Geno, one with a purple shirt and a blond ponytail was Peach, a little Weeble-like guy with his hands out in front of him was Bowser (because the hands were like Bowser clawing enemies), and a cop from another set was Smithy (because the badge on his shirt looked like the final Star Piece on Smithy's chest). A toy drum with three xylophone panels on it was the stump where you battle Bowyer (the xylophone panels were the X, Y, and A buttons that he locked). They would battle on top of speakers, by the (unlit) fireplace, on top of a globe toy, inside of a round thingie with the moving beads on the wires that represented the entire universe (or, more often, the multiverse, though I don't know if I specifically used that word back then), and all kinds of places like that. Usually Smithy would come back from the dead somehow, and once he joined Mario's party only to turn on them when the six of them got into a boss fight.
I also remember that Magical Quest Starring Mickey Mouse was the first game I ever beat.