I'd like to see it become infinite

Good solid start for a platformer. Until running into a dead end in the 2nd level, I actually enjoyed this quite a bit.

A couple small things at the time of this writing I want to point out:
* The main character cannot fall down through holes only one block wide. I'm not sure if this is intentional or not.
* Some minor animation issues brought up already in the comments.
* A death sound/animation would be nice so it's clearer that's what happened. I think the game should also make level starts/ends more obvious, too.
* Scenery always appears in front of your character. It makes sense for things like grass and flowers, but it's a little odd to see the character occasionally hidden behind houses or large rocks. Maybe these things should be placed in the foreground instead.

I'm sure more things will be added later, like enemies or hazards. This game is off to a good start though, and I would be interested in seeing how it comes along.