Very rarely, but it happens.
Some people may remember a Virginia man, featured on the cover of Time Magazine, who was executed despite protestations of innocence?
From the New York Times, Jan. 13, 2006:
DNA Ties Man Executed in ‘92 to the Murder He Denied
WASHINGTON, Jan. 12 - Thirteen years after Roger K. Coleman went to the electric chair declaring, “An innocent man is being murdered tonight,” a new DNA test has found that he was almost certainly the source of genetic material found in the body of his murdered sister-in-law, Virginia officials announced on Thursday.
The finding was a stunning blow to a lay minister who for nearly 18 years argued for Mr. Coleman’s innocence, and it vindicated the prosecutors who won Mr. Coleman’s conviction in 1982 and the governor, L. Douglas Wilder, who allowed his execution to proceed 10 years later.
“The confirmation that Roger Coleman’s DNA was present reaffirms the verdict and the sanction,” said Gov. Mark Warner, who ordered the test last week. It was the first time that a governor had ordered a DNA test involving an executed person.
The testing was closely watched across the nation because of the belief that it would provide powerful momentum to death penalty abolitionists if it were to prove that an innocent man had been put to death.
Yet even after Thursday’s announcement, critics of capital punishment said Mr. Warner’s decision set an important precedent that might encourage other governors, judges and prosecutors to allow postexecution DNA analysis in disputed capital punishment cases...
http://www.nytimes.com/2006/01/13/national/13dna.html
But, was he really guilty of murder? or just guilty of sleeping with his SIL before she was murdered by someone else??? :o)