Both ADE1.7.2 (see *** below) and ADE2.0 run on Windows 8.
ADE2.0 is full of bugs on Windows 8; but only the same bugs it has everywhere else as well.
Neither can take advantage of touch, nor run in Metro mode (whatever it's proper name is).
As far as I am aware, there is no Adobe DRM compatible app that runs on Windows RT.
Two alternatives ...
For DRM free ebooks, use the free and vastly superior Calibre. http://calibre-ebook.com/
For DRM ebooks, you can use Sony Reader; free download from Sony intended to run with Sony eReaders but works quite happily without. I prefer ADE1.7.2 to Sony Reader. https://ebookstore.sony.com/download/
*** 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-editio ns.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