Henry Lee Lucas
Henry Lee Lucas was, or perhaps wasn't, a serial killer (although he was a known wife beater, child molester, and possible necrophiliac, according to A&E's Biography), and was walking proof of just how idiotic the justice system can be when you push it. In 1960 Lucas was arrested and convicted of murdering his mother. In 1983, on trial for murder for the second time in the state of Texas, and realizing that he had no chance of a fair trial, Lucas decided to symbolically protest his fate by confessing to the murder in question, and 600 additional murders. Amazingly, not only was his confession accepted, he began being treated like a celebrity by the police.
This began a period of Lucas touring around the country, going to police precincts in various locations where murders had been committed, even when he couldn't possibly have been there at the time, just to confess and get the crime off the books. By the end he had confessed to committing 3,000 murders, generally being allowed to read the files on them first to make sure his information would check out.
While he was on death row for a while, the then-governor of Texas, George W. Bush, made one of his few good decisions and ended the whole travesty by commuting his sentence to life (the only death row inmate he ever commuted). He died of heart failure in 2001 at the age of 64.
It should be noted that, while most of his confessions were ludicrous, he was convicted of two murders, and during a few of his confessions he seemed to have information he had not been given ahead of time, so whether or not he was actually a serial killer depends on who you ask.