It was pretty good.
Make a defined background, where if you fall down the background moves up. And in a background where the differenence isn't just vertical, (and I suggest making somewhat more detailed backgrounds anyway, like outer space, or a spaceship, or something. Spice it up a little) then have the screen scroll to the left when you go to the right, and scroll to the right when you go to the left. Of course, if the background is really far away, (such as in the outer space example) then don't parallax scrolling and stay stationary.
Getting stuck in platforms is not fun, make the physics a little more detailed. If a player gets stuck between a platform and a rock, however, something needs to happen. I suggest they get sent to the beginning of the level.
Speaking of that, on some levels, when I fell down, I came back up on places which were farther forward than I was before.
Also, if the character is on a moving platform, he would move along with the platform. In the game, the character stays exactly still. And unless the character has no friction, then he would move along with the platform, and if he doesn't have friction, he wouldn't be able to walk or jump in the first palace.
I liked the way you didn't feel the need to arbitrarily jam in monsters and just kept it nice and simple. Platformers with monsters in them often end up too much like mario games. This was unique and clever. And a few more levels would be nice, heh heh heh.
Anyway, clean cut list of possible improvement:
-One or more semi-detailed background(s).
-Parallax scrolling (unless the background is really far away.)
-Better death animation (have the guy fall into a lava pit, or have the guy spin around while falling, just don't let it be boring.)
-Don't let the guy get stuck in blocks.
-While you're at it, Give "the guy" a name, Chuck or something.
-Don't come up with a cheesy story, please. Any semblance of background or story should only be a fun little addition. The player should spend his majority of time on the actual game.
-Players should begin at the start of the level when they fall.
-If Chuck is on a moving block, make him move with it.
-Keep the challenges only platform challenges, but possibly make the levels harder as you go on.
-More levels, I love platformers.
Thanks for listening. Most of these changes wouldn't take up too much data, or don't take up that much data at all.
Glad to help