“Irregardless” is likely the illegitimate love-child of two legitimate words: “irrespective” and “regardless.” It’s a favorite of TV writers who want to show a character isn’t as smart as they think they are (unless I’m remembering wrong, Paulie from The Sopranos says it on more than one occasion.)
On a related but personal note, the word has special significance for me because it’s a sure-fire way to drive my brother crazy.
Unless you’re using “irregardless” in a work of fiction to reveal character, this illegitimate word is best avoided. Irregardless of how much it tortures my brother.
