Ah, the Mario series. To me, the question of which is the best is hard to answer, because it means saying that the rest of them are not the best. I mean, take the original for example; it's a milestone in gaming, one of the first truly great games, and originator of one of the most recognizable lines of dialogue in pop culture (Thank you Mario, but our Princess is in another castle), not to mention being the first video game I ever played or owned. But then there is Super Mario Bros 2 (the American version), which is the first Nintendo game I ever saw played, as well as the first I beat on my own (I wasn't very good at the original) and added color and flavor to the cast of the Mario series.
But like the Highlander, there can be only one, and for me that one will always be Super Mario Bros. 3. You just can't beat the variety and awesomeness of its powerups, the specialization of each world, the addition of elements now commonplace in the Mario series (Boos, Thwomps, Chain Chomps, ect.), and for many of those of us who are old enough to remember its release, the nostalgia meter is through the roof. All the while, it maintained a distinctly Mario feel. In short, you cannot beat the combination of the Tanooki suit, Kuribo's Shoe, and Big Land.
Mario World comes in a close second, being so much bigger, and having elements like secret exits and Yoshi going for it, but also being set back by the lack of variety in powerups (classic Mushroom, Flower, and Star are joined the Cape; a cheap rippoff on Raccoon Mario) and no specialized worlds (No Ice Land, no Water Land, no Pipe Land).
Honorable mention goes to New Super Mario Bros. for trying to bring back the platforms. Now, if they could just ditch the crappy music, replace Mario's obnoxious voice with the original jumping noise, and toss about six or seven new suits and some Mario 3 lovin' we might have a new contender.
