Probably a blend of irrespective and regardless, irregardless means the same as—and is a hyperbolic form of—regardless.

It is regarded as incorrect in standard English, because the negative prefix ir- merely duplicates the suffix -less, and is therefore unnecessary.

The earliest instance that I have found is from a poem titled The Old Woman and her Tabby, published in the City Gazette & Daily Advertiser (Charleston, South Carolina) of Tuesday 23^rd June 1795; this poem comes immediately after Mrs. Pindar’s Reply to Husband Peter, a paragraph in which the author, after explaining why she does not like dogs and why cats are her “delight”, concludes that “there is a moral obligation between a human being and a cat”:

In a cottage remote from the noise of the town,
Did pious Old Betty contented reside,
(Her station no higher enjoyments could crown)
With Tabby, her constant companion and pride.

Full fifteen long years they together had liv’d,
Unacquainted with shyness, division and rage;
The sight of each other high transport reviv’d,
And their friendship grew stronger and stronger by age.

When eating her milky repast at the door,
Now the beautiful sun had sunk gently to rest,
She would cry, resolv’d not to taste a drop more,
“Come, pussy! poor pussy!” and give her the rest.

Thro’ the long Winter ev’ning together they’d sit;
While the tempest, loud howling, tore limbs from each tree;
And with her sole friend lying close to her feet,
Conceiv’d none half so blest as her Tabby and she.

But death, irregardless of tenderest ties,
Resolv’d the good Betty, at length, to bereave:
He strikes—the poor fav’rite reluctantly dies!
Breaks her mistress’s heart—both descend to the grave.

The second-earliest instance of irregardless that I have found is from The Morning Post (London) of Friday 30^th July 1847, which transcribed a speech that Lord Thomas Clinton had delivered the previous day during the nomination of candidates for the representation of Canterbury:

He came forward on purely independent principles. (Cheers.) He was not bound to support any party in the House; neither was he biassed [sic], bigoted, or antiquated. (“Hear, hear, hear,” and cheers.) He was quite willing to go forward as the corrector of those abuses which really did exist, and the removal of which would be beneficial to the interests of the country, but he was decidedly opposed to those ill-advised and useless innovations, brought forward irregardless of the dangers and injuries they might inflict on the country. (Hear, hear.)

Another early occurrence is found in The Daily Union (Washington, D.C.) of Friday 13^th July 1849, which published a letter in which “An Old-fashioned Whig” objected to the removal of Major Edmund Christian from the office of marshal for the eastern district of Virginia:

Why, then, has he been removed? Has he not done his duty? Has he not proved himself “honest, capable, and faithful?” Has any offence been alleged against him? Or is it because the bloodhound spirit of an office-seeker will track any victim so that he can but secure the spoils irregardless of any incumbent, however faithful, honest, or competent he be?

In a prescriptive approach to language, irregardless is often regarded as simply not being a word—which makes no sense, since it has been in use for over one hundred and seventy years.

For example, in Irregardless, it’s not a word, published in the Statesman-Journal (Salem, Oregon) on Tuesday 4^th November 1986, William Florence does not seem to realise how ridiculous his refutation is, for, instead of considering irregardless in its real usage, he contents himself with appealing to a prescriptive opinion on this word, (ir)regardless of its usage:

A reader recently requested a reminder for all who care about such things that this awkwardly and improperly constructed combination of regardless and irrespective really doesn’t properly exist as a word at all and should be retired or relegated to some minor league team’s bullpen.
Quite right, we responded, calling the fabrication an abomination.
That brought a hoot and a scowl from one outraged reader, however. He was quick to declare that we were priggish and should be relegated, in his words, to the prigpen.
“Regardless, or irregardless, of what you and other self-appointed/anointed arbiters of the English language may say about the nonstandard word irregardless, pardon me if I defer to Webster’s,” he indignantly wrote.
“As you can see from the enclosed photocopy of that dictionary’s explanatory notes (Ninth New College, 1984 edition), irregardless is an adverb which from a stylistic standpoint is considered to be nonstandard.
“This means that its use is ‘disapproved by many.’ But irregardless of that, it nonetheless enjoys ‘some currency in reputable contexts.’
“Obviously, then, while style-wise elitists such as yourself may not use irregardless, it is perfectly all right to do so. The abomination is your pompous assertion to the contrary.”
All of these assertions reminded us of John B. Bremner’s entry under irregardless in his book Words on Words, however. Bremner writes:
“Regardless of the school of a-word-is-a-word-if-the-people-utilize-it, there is no such word as irregardless, except when used for hyperbolic humor, and even then it isn’t very funny.”
It would seem, then, that our trip to the prigpen is a short one.