If something is done without consideration, it's done regardless, usually followed by the word "of." Today you can sit wherever you'd like on a bus, regardless of your race, but this wasn't always the case.
The word regardless can also be used as an adverb meaning despite everything. If your speaker had to cancel, you should carry on with the meeting regardless. People sometimes use the word irregardless when they mean regardless. Irregardless is an error resulting from a blend of irrespective and regardless. You may hear people say it, but grammarians consider it to be a mistake.