Your regedit.exe file may have become corrupt or altered by some sort of virus or spyware. I would first try the usual virus and spyware scans.
If that doesn't help you can get a backup copy of regedit.exe from your C:\WINDOWS\system32\dllcache folder and overwrite the one in your C:\WINDOWS folder.
Another option is to delete the contents of your prefetch folder to get rid of any faulty version of regedit that is loaded when the computer starts. The prefetch folder is used to help speed up the loading of programs by loading programs it thinks you might need. It is located at C:\WINDOWS\prefetch. It is ok to delete the contents of this folder just don't delete the folder itself.
Another thing to try from the run menu is to type regedit.exe rather than just regedit. Sometimes this will make it work.