Google has added the ability to upload your own ebooks to Google Play Books. This means you can upload your own files and read them on any of your devices with the Google Play Books ereader app installed.
You can upload up to 1000 EPUB or PDF files, or import files you already keep in Google Drive. Once uploaded, you can read your books in the browser, from the Android app, or iOS app. Your page position, bookmarks, and notes are all synced across all of those devices.