Tina Turner did it, as well as Denise Rich and Eduardo Saverin.
As U.S. taxpayers expatriate at record rates, some experts say a complex IRS tax code could be to blame.
So far this year, 2,369 people have either given up their U.S. passports or surrendered their green cards after long-term residency, according to Andrew Mitchel, a tax lawyer in Centerbrook, Conn., who watches the data closely.
(Read more: U.S. expats reach record in 2013)
The number represents a 33 percent jump from the previous record, set in 2011, when the Treasury Department published the names of 1,781 expatriates. With another quarter to report, this record-breaking total likely will go even higher.
Root cause of the exodus
Experts say an overly complex tax system could be driving some Americans to throw in the citizenship towel. Some expatriates are also subject to an exit tax.
Mitchel attributed part of the exodus to "the IRS cracking down on people with overseas accounts."
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"All this publicity has really made people more aware of these U.S. tax obligations and all of the penalties that can go along with not filling out the forms," he said, adding that penalties can be large enough to bankrupt even the wealthy.
Unlike many countries, the U.S. taxes people based on citizenship rather than on residency. That means that if you move outside the country, you still have to file with the IRS, a process that can end up costing thousands of dollars.
"With the new regulations, it's too ... easy to commit errors," said Shaoul Aslan, a partner at Patton Boggs in Washington who heads the law firm's immigration and nationality practice. "People are tired of that—and not as much the saving of taxes as people not wanting to commit an error."
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Because people are not required to state why they are renouncing their citizenship, San Francisco-based lawyer Robert W. Wood said it may be overstatement to say it's always—or even usually—for tax reasons.
Still, he said, most expats do express frustration over a byzantine U.S. tax system.
"I think when some people say they're doing it for tax reasons, it may not be because of a high-dollar amount but rather the complexity," Wood said.
The move also solves a common frustration for Americans living abroad, he said.
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"They don't want to have to tell foreign banks that they're an American, because the banks often don't want American money in the bank," Wood said.
That attitude stems from the Foreign Account Tax Compliance Act of 2010. It requires U.S. taxpayers to report information about certain foreign financial accounts and offshore assets, and stipulates that foreign banks register with the IRS and report information about accounts held by U.S. taxpayers.
"Instead of simply putting the burden on taxpayers to report, it also requires banks to inquire if someone is a citizen or not," Wood said. If they are, the bank has to verify that they are reporting.
A somewhat significant downside
Although expatriating relieves former U.S. citizens of complicated reporting, Aslan at Patton Boggs pointed out a drawback.
"My problem always has been that you then have to go get a visa to come back to the U.S.," he said. "There is a risk that the U.S. government won't let you back in."
Mitchel pointed out that if a person is subject to the exit tax, it can complicate inheritances, and pensions can be subject to major tax penalties.
A separate law, the Reed Amendment, could present a huge hassle for those who choose to expatriate, as it lets officials stop any person who renounced citizenship for tax purposes from entering the country. To Mitchel's knowledge, it has never been enforced.
—By CNBC's Katie Little. Follow her on Twitter @KatieLittle.