During a backup using WinRescue Vista I received an error message, "Out of Memory".  Anyone have a suggestion how to proceed?

   You probably ran out of space on one of the drives.  WinRescue uses a temporary directory to construct the backup.  It is probably the drive that has that temporary directory that is running out of space.  Look at the Temp setting in the Advanced section of Backup Properties to find out which drive that is and to set it to a different drive.

Same "out of memory" message.

Winrescue runs full backup to 84% but says x amount of files copied and operation completed but when completion popup is closed the "out of memory" message box shows up.

Temp directory is on drive with 100's of gigs of free space.

   There also needs to be enough free space on the drive you are putting the backups.
   Another possibility is that the backup is just too big for WinRescue.
   It is normal to get the error message after the Backup Complete message even though the error actually happened before it.

Have beau·coups of drive space.

"Another possibility is that the backup is just too big for WinRescue"

Uncompressed backup is <18 gigs so just what is too big?

   18 gigs could be too big.  I try to keep my backups under 5 gig.  Some make backups much bigger than that.
   WinRescue is mainly for backing up the registry and other important files.  It works best when you limit it to that.