The actress Elizabeth Montgomery, who is most famous for playing Samantha Stephens on the television series Bewitched, didn't believe that she could sing very well. Nevertheless, she sang occasionally, and even sang on a couple episodes of Bewitched.
She danced to a vocal version (!) of the theme of Bewitched on the ABC television show The Hollywood Palace (below), and appeared on the cover of the Now Hear This! compilation (above).
Scroll down for more examples of Montgomery singing with Vic Damone and on Bewitched.