Baseline (Widescreen) Solution & Issues
1280x720, 1280x768, and 1280x800 are supported natively and are automatically selected depending on your desktop resolution's aspect ratio.
If you really want to, you can force a resolution with the command line parameters "-width XXXX -height XXXX" but that's probably not worth the trouble - this is a 2D game, and higher resolutions are just upscaled anyway.
Ultra/Super-Wide (21:9/32:9) Specific Solution & Issues
Stretched; some users report part of the screen cut off.
Eyefinity / Surround Specific Solution & Issues
You can force surround resolutions through the command line, but it's bugged.
4k UHD Specific Solution & Issues