Yes, he is. Under British law, a commoner is anybody who is neither the Sovereign (ie. the reigning queen or king) nor a peer. Prince Harry, is currently neither.
When his brother Prince William was married, he (William) was given the title Duke of Cambridge (ie. a peerage) and as such ceased to be a commoner.
Harry, however, remains a commoner.
By the way, commoner is not to be confused with the pejorative British term 'common' which refers to a person who is brash, vulgar and unrefined.
(on edit) The above answer is totally untrue!!! Prince Henry (Harry) is NOT a commoner. He is a Royal Prince. So was (and still is) Prince William. Where do people get these stupid answers from????
(further edit for clarification)
The Oxford English Dictionary defines commoner as, among other things, someone who is not part of the aristocracy or royalty. Prince Harry (Henry Charles Albert David, or Prince Henry of Wales) does not fit under this definition of commoner, and OED contains a highly reputable collective of researchers.
Keep in mind, too, that royalty experts worldwide prefer to avoid the word commoner as it has dropped out of favor of official British law. See the related links below for more details.
Prince William married Miss Catherine Middleton (a commoner) on 29 April 2011. In British law, strictly speaking, a commoner is anyone who is neither the monarch (King/Queen) nor a peer (Duke, Marquess, Earl, Viscount or Baron/Lord.) Prince William was a commoner before he was made a Duke; Prince Harry still is a commoner.
Yes he is currently dating his off again on again girlfriend who is indeed a commoner: Chelsy Davy
Prince William is of royal blood, hence, not a commoner.
A commoner.
He was naught but a commoner. The Prince married a commoner. I am a commoner. Commoner refers to the regular masses of people without rank or elevated status.
A commoner who finds a genie and wishes to become a prince.
Princess Catherine is a commoner, but I did no research on it. I just saw the headlines of the news when her and Prince William got married. It said Commoner Kate is marrying Prince William.
Prince Harry is not married
the prince is planning to abdicate the throne in order to marry his love, who is a commoner
Prince Harry
Prince William's brother is Prince Harry.
Prince William's brother is Prince Henry Charles Albert David better known as Prince Harry.