Error from Program Compatibility Assistant when installing SQL Server 2008
From Mark Sinkinson's enigmatic comment, you'll notice that that earlier versions are not compatible on Windows 8. 2008 &amp; 2008R2 are supported, but you need to update them to their most recent service packs.

I agree though, Program Compatibility Assistant isn't the most assisting.

Basically, you just need go through the "Run the program without getting help" option, and then when the installation is finished apply the most recent Service Pack (2 for 2008R2, 3 for 2008).

This MSDN blog post goes into further details on this.

Not really your question but you might want to head over to Brent Ozar's website for a handy checklist/guide for SQL Server installations. I've done quite a few of them but still have that to hand whenever I do a new one.