I know everyone seems to like DropBox, but SugarSync has had an Android app for some time now that works great in full screen on the eDGe without modification. Essentially the same kind of thing as DropBox, with a free 2 GB option, etc., and I don't know which is "best". I just use it for access to my Calibre library and for that it works perfectly (except that Calibre keeps covers separate, so they're not transferred with the ebook, not SugarSync's fault though).

https://www.sugarsync.com/downloads/android.html