Released at the start of the Disk System's timeline, Super Mario Bros. 2 was its most popular game, with a total of almost 2.5 million copies being sold or read onto - meaning that a sizable percentage of Disk System owners all had this game, making it pretty common these days. Most you'll find now are copies - as SMB2 takes up only one disk side, it's common to find it on side A and something like Golf or Volleyball on side B.
The plot is unchanged from the first Mario, and to be honest this isn't really a sequel to the first classic as much as another 32 levels for you to bounce Mario around in. Unlike the first, though, these levels get hard right from the start and don't let up until the very end. You really have to search for all of the power-up mushrooms from 1-1 on as very few of them are actually in ? blocks.
What are in the ? blocks, though, are the evil, putrefying poison mushrooms. If Mario should be unfortunate enough to hit a block containing one, he better stay as far away from it as possible, for it knocks him down from Super to Regular Mario, or kills him if he's already Regular Mario, if he touches it. And you don't even get any points for your anguish!
Besides these, and a few added bits to gameplay, the game plays very much like the sort of add-on to the original SMB it is. Later levels have wind blowing around in them, and it's amusing to make these huge wind-aided jumps (the wind isn't random, either, like in Ninja Gaiden II). One level consists almost entirely of bottomless pits and super trampolines that put Mario in the air for about ten seconds. If these kinds of weirdo levels were put in the first game then SMB probably wouldn't have sold half as much as it did, but with the Disk System sequel the designers has more leeway (did I mention that there are Bloobers swimming around in the air in some levels?).. and with that new freedom they made eight fairly fun new worlds.
Or are there more? This game is filled with new secrets, not to mention a hidden world or two. For hints and screenshots, check out the SMB2 Notes.