I don't have an Android reader application
'Android reader application' myself, but some features that I find important in my e-Reader (Sony Reader PRS-650) are:
- Ability to organize books into collections (or tagging could be a substitute)
- Dictionary (double tap a word and look it up)
- Ability to annotate/take notes
- Ability to adjust zoom level, margin cuts, font sizes.
- Brightness control.
Almost forgot. The supported ebookeBook formats is important as well.