I lived through Mario taking over the world and it's really no mystery; the main line Mario games have been universally really solid. The one black sheep, Super Mario Sunshine, is still a solid game it just was too big of a change from Mario 64 for people to handle at the time.

Particularly Super Mario Bros 1, Super Mario Bros 3, Super Mario World and Super Mario 64 really pushed games forward. Each one of them really opened up new possibilities in games that the rest of the industry was influenced by.

The amazing thing is that Nintendo did that with the Zelda series as well, but this thread is about Mario.