I guess I haven't contributed to this thread yet.
My favorite 2D platformer is New Super Mario Bros. Wii, followed by Super Mario Bros. 2. Wii had multiplayer and mods; I even worked on a mod for New Super Mario Bros. Wii which changed the Toads into the Baby Mario Bros. which increased my enjoyment of the game tenfold, as well as modding the music and voices. Had so much fun both playing it, playing Newer, and enjoying it with all of that.
Super Mario Bros. 2 USA (specifically the GBA version) is my favorite of the classics because playable Toad, no time limit, allowing you to mess around in levels in your own pace and encourages some exploration (such as the trial and error Yoshi eggs in the GBA version but because the potions are trial and error, can be annoying to get at points) and picking and throwing enemies is just fun. The bosses aren't that special but I did enjoy all of them. The soundtrack is only like, three pieces but it's pretty average at the time and I still enjoy the music it had.