Irrespective is a word, unlike irregardless which is not a word. This doesn't stop people from using it, because it sounds kewler. Both the word and the nonword mean "in spite of everything; without regard to drawbacks" according to Princeton University, but what do they know? Other words that are suitable replacements for the word irrespective or the nonword irregardless include regardless, irrespective, disregardless, no matter, and disregarding. All of these words and phrases mean pretty much the same thing; without or in spite of regard for something or other. In fact it's rather silly to have so many words that mean the same thing. The eskimoes have forty-seven words for what the rest of the world calls snow. I guess they know what they're doing.