Browsing the different SketchUp Help Forums, it seems that SketchUp users nowadays often have the question whether "SketchUp supports Windows 8". Although the answer is not "official" by the SketchUp Team - as you can read in this Help Group post by Patrick: "SketchUp Pro 8 doesn't officially support Windows 8. However, we've been doing extensive tests and we haven't found any significant issues yet...", from my own experience, SketchUp (8 that I have installed here at least) supports Windows 8 (64 bit) perfectly.
Probably most important thing is the video driver - i.e. if your video card has an up-to-date, fully OpenGL compliant driver. I have an NVIDIA GeForce GT 640 which runs SketchUp 8 Pro (and LayOut) like charm. Of course, do not expect that your Windows 8 will run SketchUp on a Tablet device or similar - use a good, old (or new) PC without all the fancy touch-screen functions.
The only thing I could not get to work exactly as it used to work on my old, XP installation is the "SketchUp Full Screen Plugin" - which I would mainly use for setting chromeless windows and hiding toolbars when creating tutorials anyway - so the lack of this functionality will not affect my productivity at my modelling workflow at all (still wish to see it work of course).
For the full, official list of hardware and software requirements, please, refer to this Help Center article.