From our friend Pat Merrill, 
publisher of ENcourage Newsletter, in Scottsdale, Arizona:

"I had occasion to research this to a light extent recently, in response to an inquiry in a nationwide newsletter which I publish in regards to panic disorder/agoraphobia. Other "famous folks" that (according to other articles) have or do suffer from an anxiety problem include: Carly Simon, Aretha Franklin, Lani O'Grady (actress), Michael English (Gospel artist), Sir Laurence Olivier, Earl Campbell (Heisman Trophy winner), Al Kasha (songwriter, Emily Dickinson, Marty Ingels and probably many more.

According to the "Leeza" show, Nicolas Cage and Roseanne have also had such difficulties.  Naomi Judd and Susan Pewter have spoken of having had an anxiety attack, but I suspect they were one-time experiences.  Hope this is accurate and of help in your research."

Other famous people who have mentioned having problems with anxiety include:

John Madden

Leila Kenzle

Sally Field

Shecky Greene

Alanis Morisette

Burt Reynolds

Kim Basinger

Olivia Hussey

Tom Snyder

Sam Shepard

Isaac Asimov

Charles Schultz

Barbra Streisand

Anne Tyler