New York Times v. Sullivan:

The First Amendment "prohibits a public official from recovering damages for a defamatory falsehood relating to his official conduct unless he proves that the statement was made with 'actual malice' -- that is, with knowledge that it was false or with reckless disregard of whether it was false or not."

Gertz v. Welch:

"We hold that, so long as they do not impose liability without fault, the States may define for themselves the appropriate standard of liability for a publisher or broadcaster of defamatory falsehood injurious to a private individual."
"[W]e hold that the States may not permit recovery of presumed or punitive damages, at least when liability is not based on a showing of knowledge of falsity or reckless disregard for the truth."