Parallels, Inc. announced September 26 that Parallels Desktop 9 for Mac is the only Parallels version available today that will support Mac OS X Mavericks. If you are running an earlier version of Parallels on your Mac and wish to upgrade to Mavericks, you should upgrade to Parallels Desktop 9 for Mac before upgrading to Mavericks.
Visit http://new.roaringapps.com/apps?index=a for an app compatibility table for Mavericks.