If the book does not use DRM, then yes you certainly can.
(and you don't need ADE on the computer to read it either, you can use a program such as Calibre)
If the book is DRM, you can as long as the eReader support Adobe Adept DRM.
Most do, but some don't (especially Kindles, and some very budget models)
If the ereader is a tablet you may need to install compatible reader software such as Bluefire or Aldiko (or it may come preinstalled)