Another was the Shakespearean actor Laurence Olivier, who was known to regularly vomit before each stage performance.
All share the same "fight or flight" response -- the brain's reaction to perceived danger.
That mechanism normally serves as a protective function, but during a panic disorder, a switch in the brain turns it on when there is no real threat. Attacks are part-biological and part-learned, and they tend to run in families.
"All of a sudden they get a burst of anxiety and they don't know why and where it is coming from," said Jeff Szymanski, director of psychological services at the OCD Institute at McLean Hospital in Boston, one of the nation's leading psychiatric centers. "It's very frightening and feels like something is wrong with their body."
Experts say sufferers shun situations where they have experienced fear -- an elevator, a crowded room or, in the case of these celebrities, performing. It becomes a vicious cycle, their brains then reinforce the avoidance response. When left untreated, these attacks can escalate.
Stage fright is one of the most common forms of anxiety disorder -- though some anxiety is shown to be helpful in performing. "One study showed fear of speaking in public was higher than fear of death," said Szymanski.
He said that "facing your fears" is the most effective way to eliminate panic attacks. So-called exposure therapy slowly reintroduces the patient to the feared scene or object.
In Simon's case -- spanking before performing -- can be helpful, though unconventional, said Szymanski, who has not treated her.
"If you think about anxiety, there is a thought or component that exacerbates it," he said. "Carly Simon said, 'If I can do something that gets me into my immediate sensory experience, that keeps me focus on the right now.'"
Medications can sometimes help a patient "get more put together" so they are willing to undergo treatment, according to Szymanski.
But while exposure therapy followed by talk therapy is highly effective, it has the highest drop-out rates. "Most don't want to do it," he said. "They say, 'Give me a pill that makes it go away,' and try to find a way around it."
Panic attacks tend to occur alongside other mental or physical illnesses, including depression or alcohol or substance abuse, which may mask the underlying condition. Many people learn to fear the fear itself, inducing panic attacks through "auto-intoxication." Others believe they are having a heart attack, losing their mind or on the verge of death. They can occur at any time, even during sleep.
Actress Nicole Kidman explained her panic attacks to Vogue magazine in 2002: "I panic in front of all the cameras. My hands start shaking and I have trouble breathing. Tom [Cruise] would always whisper to me that everything was all right."
Willard Scott, spokesman for Smucker's Jam, described his attacks that began decades ago when he was a weatherman for NBC's "Today Show."
"I was sweating profusely, I couldn't breathe, my mind was befuddled. The people in the studio called a doctor because they thought I was having a heart attack," he said.
Sometimes panic attacks are rooted in childhood trauma, according to Helen Resneck-Sannes, a California psychologist and author of "There Really is Something to Be Afraid Of: A Body-Oriented Psychotherapy for the Treatment of Panic Disorder"