Roscoe Orman, the actor who's played Gordon on Sesame Street since 1974, was ordered by a judge to continue paying palimony to the mother of his four kids, even though the unmarried couple never had any kind of written agreement about it.
Orman—who looks amazing for 71—broke up with Sharon Joiner-Orman in 2010 after four children and 39 years together. He married another woman in 2012. A judge said that through his deeds and words, Orman had acknowledged a palimony agreement, and ordered him to continue paying. Orman's lawyer plans on appealing, since a 2010 law in New Jersey requires that palimony agreements be in writing.
DISCUSSION
So to save everyone the trouble of googling Palimony like I just did, here's Wikipedia:
Divorce.com has more info as well.
edit: I realize the article does make it clear but I feel like the term was just sort of dropped as if everyone knows what it is, and I didn't feel like I quite understood it after reading.