Super Mario Bros on the NES. I grew up on Mario, which is why I was a Nintendo fanboy until the Wii hit. Believe it or not, the game that introduced me to RPGs was Super Mario RPG for the SNES. This just goes to show that I have fond memories of the Italian plumber who put Nintendo on the map. Even though Nintendo's shift towards casual gaming has caused them to lose support from the hardcore crowd, I'm still excited for New Super Mario Bros Wii. I'll have to be careful who I play it with, though. As I've seen from watching a session some friends of mine were playing, some people are less concerned about getting through the game (which is significantly challenging, unlike the DS New SMB) and more concerned with sabotaging the other players.
When it comes to classic Mario, I personally prefer single-player or co-op rather than competitive play.