I am aware of Henry FitzRoy, his illegitimate son that he acknowledged whom he had with Bessie Blount. Are there any other confirmed illegitimate children?
Henry Fitzroy is the only recognized illegitimate child recognized by Henry VIII.
Henry FitzRoy, 1st Duke of Richmond and Somerset (15 June 1519 – 23 July 1536), was the son of King Henry VIII of England and his mistress, Elizabeth Blount, and the only illegitimate offspring whom Henry VIII acknowledged.
Other children who were suspected as being illegitimate offspring of Henry VIII are Catherine Carey, who was the daughter of his mistress, Mary Boleyn. Most historians agree that Catherine was his daughter, hence the timeline of her conception, her "Tudor" red hair and the fact that Henry VIII took an interest in her education and upbringing. Also, Catherine was a favorite of her cousin, Queen Elizabeth I. I believe Elizabeth I believed Catherine to be her sister rather than her cousin.
Catherine's mother was Mary Boleyn, a mistress of Henry VIII before he courted and later married her sister, Anne Boleyn. Catherine is believed by some authors to be an illegitimate child of Henry VIII.
Catherine's brother, Henry Carey is also rumored to be offspring, although he was conceived after Mary Boleyn married and the king tired of her, so it is highly unlikely.
The son of Mary Boleyn, he was a cousin of Elizabeth I. Since his mother was also a mistress to King Henry VIII of England, some historians have speculated that he might have been an illegitimate child of Henry VIII.
John Perrot, Thomas Stucley, Richard Edwardes and Ethelreda Malte were other "rumored " illegitimate children; however there is scant evidence for these.
An interesting fact is that Mary I and Elizabeth I were actually deemed illegitimate by Henry VIII due to succession rights.