title_body: Is there an Android reading app that synchronizes across devices?
upvoted_answer: Moon+ Reader can do this, storing the data in Dropbox or in Google Drive.
  
  (Note: I have not actually tried this functionality myself as I can't bear to use Moon+ due to its horrible UI and poor support for the ePub standard. But the feature is there in the settings, if you can find the right settings page...)
  
  Google Play Books does so too - but it does not directly open files stored on the device (you have to let it upload them to Google's servers and then download them again...)