Coverjunkie asked great art director Robert Newman about the 5 most favorite covers he designed himself:

Robert's favorite #1: The Village Voice, October 12, 1993.
Illustration by Stephen Kroninger. "We really hated Rudy Giuliani at The Village Voice, but we put him on the cover as often as possible because he always sold a lot of issues. I think this illustration captures the essence of Rudy's evilness."

About Robert Newman:
Robert has been a design director at a wide range of consumer and trade publications on big names like: New York magazine, Details, Entertainment Weekly, Vibe, Real Simple, Fortune, The Village Voice & Guitar World.
He and his teams won numerous publication design awards and medals. In 2004, AdAge magazine named his Real Simple team the Creative Team of the Year. Right now he's a design and content consultant for numerous publications like JCK magazine, Newsweek, O: The Oprah Magazine, Reader's Digest, TV Guide and many more.
Robert also was past president of the Society of Publication Designers, has been a frequent guest lecturer at the Poynter Institute and speaks regularly to groups and conferences about publication design and art direction.

A must see:
Don't forget to check (plus a big thumbs up) Robert's Newmanology page for your daily updates on magazines, covers and other ace mag stuff.