Pun for the Ages. "The inglorious pun! Dryden called it the 'lowest and most groveling kind of wit.' To Ambrose Bierce it was a 'form of wit to which wise men stoop and fools aspire.' Universal experience confirms the adage that puns don't make us laugh, but groan. It is said that Caligula ordered an actor to be roasted alive for a bad pun."
My beef is with dumb oxes who say "pun not intended" to an intended pun.
I think that much of the time when people say "no pun intended" even when it was intended are helpfully pointing out a pun that would otherwise have gone unnoticed. Some puns are not obvious, partly because people are not looking out for them or paying close enough attention to what a person is saying. Nobody wants to waste a pun! And some puns are unintended, with the speaker not noticing until it has been uttered. Saying "no pun intended" is an acknowledgement of that.
If I remember correctly, back in the days of word play during Beatles interviews, Ringo Starr said, "A pun is the lowest form of humor only if you didn't think of it first."