I was raised on Nintendo. Because of limited budgets I could only have one console a generation and I almost always chose the Nintendo console. I was so tired of buying flops (Game Gear and Saturn) that I didn't bother with the Playstation or XBox. But I have favorites on that console too (old-school Crash Bandicoot ftw). So I'm sorta apathetic towards games that aren't on a Nintendo console with several notable exceptions. Enough exceptions to make me want a 360. Love X Box Live Arcade. But back to the supreme plumber.
You gotta experience the very first, available on the Wii's Virtual Console (or on emulators if you don't wanna pay). The first three Super Mario Bros. on the NES but be careful that there's the Nintendo Hard original SMB2 and then there's the Doki Doki Panic clone SMB2.
I love ALL his platformers but I have special love for SMB3, Super Mario World 1&2. Although the second SMW is more of a Yoshi game. But you
gotta play Super Mario 64, the game that set the standard for 3D platforming. Super Mario Sunshine is...kinda forgettable, I loved it but not as much as the others and it's a bitch to get 100% completion on that game.
Both Super Mario Galaxy games. Play them. At least the first one. The second one is awesome too, since it has Yoshi.
If you're looking for RPGs then go get Super Mario RPG: Legend of the Seven Stars. Developed by Square, with a great cast and memorable battles. Oh, and the Paper Mario games. I like them because of the unique art style.