The New York times has a great article about the clerk who has sent out notices for jury duty for the last billion years in the city, Norman Goodman, and the many bizarre responses from celebrities to being selected.

This is largely irrelevant to giving up, except that it's just so freaking funny. You have to read about what Woody Allen did.

Woody Allen sent a note, in cramped printing, protesting that he had been so traumatized by his experience in court during a child-custody dispute with Mia Farrow that returning to sit on a jury was out of the question.
...
Mr. Goodman, a strong believer in equal treatment, insisted that Mr. Allen show up, bad memories and all. Mr. Allen arrived wearing what Mr. Goodman describes as "army fatigues and a Fidel Castro cap," surrounded by his lawyer, his agent and a bodyguard. Mr. Goodman escorted him to the jury room, where Mr. Allen insisted on standing, rather than sitting like everybody else. The rest of the jurors gawked at him.

"We eventually offered him the opportunity to get out of there," Mr. Goodman said. "Frankly, we were glad to get rid of him."

That has got to be the absolute best way ever of getting out of jury duty. My god, I still can't stand him because he's a creepy pedophile and all, but damn, that's some good humor.