If this is not a platformer, then I strongly recommend adding depth to the scene.  Study the design of old cartoons, since they had to work with the same sort of limits as side view video games.

I took the liberty to pasting your character into the background of Donald's Vacation, a 1940 Donald Duck cartoon.



The lines I drew roughly break the image into the foreground (lowest stripe), the character area (between the cyan lines), the middle ground (up to the red line) and the background (everything else).

The lone tree in the middle ground serves to break up the composition into different areas (clearings in this setting).  With the character wandering horizontally, it helps to pace the scene; things happen over here (on one side of the tree), and over there (on the other side), and the character walking in front of the tree is transitioning between the spaces.

The middle ground area also contains scenery objects the character interacts with.  Doors, or treasure chests, or whatnot would be placed there.   Putting a scenery object in the character space is used only when that object also blocks further movement in the horizontal direction, or transitions to another scene entirely.

The character will generally never leave the character area, but it looks like they could.

Observe the huge jump in scale between the middle ground and background elements.  Those background elements are very far away, which emphasizes the character is unlikely to interact with them.   Also consider out the saturation differences.

Of course, if you are creating a run and jump platformer, most of this advice is moot.  More animation backgrounds are here:

http://animationbackgrounds.blogspot.com/

Hope this helps,
Tourist