Epub's

You need Adobe Digital Editions for Adobe DRM .epub files.

http://www.adobe.com/uk/products/digital-editions/download.html

You may prefer the older version which is less bug-ridden than the terrible current version. (see below)

I suggest the free Calibre for non-DRM .epub files.

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There are lots of bugs in ADE2.0 (and 2.0.1).  Try replacing ADE2.0 with the older but more reliable v1.7.2.

(You can have them both installed at once if you like.)

Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.

http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editions.html

The forum software is sometimes corrupting the link above.  There shouldn't be a blank in 'editio ns.html'.  The following redirects to the same page: http://tinyurl.com/diged172

Some people have found ADE trying to upgrade automatically. 

It appears (not 100% sure) that if you install ADE2.0 as a new install (not as an upgrade) that your 1.7.2 will continue to run.

Probably best to say no if 2.0.x installation asks if you want to migrate your library.