Espacenet (run by the European Patent Office) and Patentscope (run by WIPO) are both databases through which you can search for patents and patent applications. I believe Patentscope has somewhat greater coverage. In this sense, they are both quite similar to Google Patents.
The European register is the legal register of all European patents and patent applications. It is primarily used for confirming the status of a European patent or application, and looking at the correspondence that occurred during prosecution.