At the risk of being pendantic...
Donkey Kong began it all.
Mario Bros. gave us multiplayer.
Super Mario Bros. gave us the 2D, side scrolling, brick-smashing, power-up based gameplay.
Super Mario Bros. 2 / USA gave us multiplayer distinctions and a hefty emphasis on picking up items.
Super Mario Bros. 3 gave us the overworld, item inventory, flight, a "real" two player mode with an emphasis on competition, the Koopa Kids, and the general "modern standard look" for the Mario characters.
Super Mario World gave us Yoshi, save games, and silly things like midway points.
Yoshi's Island gave us 100% completion requirements, fleshed out Yoshi flutter jumps, and... a lack of multiplayer.
Super Mario 64 gave us "objective based" gameplay, 3D worlds and mechanics, and the concept of a "health bar."
Super Mario Sunshine gave us...... ummm.... I'm not sure what it brought that was "new" to the table, really. Gadgets?
New Super Mario Bros. brought BACK traditional, SMB-style gameplay and mechanics... and not much else, really.
Super Mario Galaxy represents the best refinement of the SM64/SMS system... and the reintroduction of the Super Mushroom and Fire Flower to the series via 3D. Powers return!
New Super Mario Bros. Wii brings true multiplayer gaming to the Super Mario Bros. series.