Skype will work on Windows 8. However, if you install it directly from the Skype website, the software may throw an error when it tries to log you in. Here are the steps that I completed (these will need to be done on the Desktop):

1. Uninstall any previous versions of Skype
2. Remove all references to Skype from the following folders: ProgramData, ProgramFiles, Users/[username]/AppData/Roaming. These folders are hidden by default. To view them, enable the “Hidden items” checkbox in Windows Explorer. This option is found in the “View” tab (on the right hand side of the ribbon).
3. Download and install the latest (as of 9/20/2011) from http://download.skype.com/msi/SkypeSetup_5.5.0.117.msi. When downloading, I saved the file to my local folder and installed from there.
4. It seems like you need to launch Skype from the Start menu (the new Metro style interface). If may crash if you launch from the Desktop.

Notes

Windows Developer Preview Build 8102

Sources

http://community.skype.com/t5/Windows/Windows-8-Developer-Preview/td-p/156212