The Lost Levels is famous for being Mario's most difficult adventure. Unfortunately, I missed out on this Japan-only sequel upon its release. The Lost levels (aka Super Mario Bros. 2 in Japan) didn't come here for a reason: the game is too similar to the original, and it's difficult as hell. This game features far more obstacles, nerve-wrecking jumps, and poison mushrooms that will instantly kill you. Also, enemies are far more plentiful, and there are new obstacles like wind and rain. If you thought Super Mario Bros.' second quest was too hard, don't even attempt this game. It's long-winded, and will test the patience of all but the most hardcore.
Like Super Mario Bros., The Lost Levels includes eight unique worlds. If you manage to beat those without using any warp pipes, then you get to experience a 9th world and worlds: A, B, C, and D. Unlike the first Super Mario Bros., you can actually save between each level (in the All-Stars version), so you don't have to start whole worlds again when you run out of lives. This makes the game a bit easier, but I believe that this featured wasn't included in the original Famicom version.
As you can see, The Lost Levels is basically Mario 1.5 with a difficulty level that is exponentially higher than the original. The Lost Levels does have some unique level designs--there are trampolines that will launch you high into the air above the screen and you have to land at the right time on small platforms. You'll also have to deal with wind and rain, but It's a fun game if you're a sadist that is able to avoid Bowser's devious traps. I managed to beat it in a few hours, so it is doable, but if you're a person that has little patience for difficult 2D platformers, you'd be better off playing any of the other three NES Mario games.