In general, the answer has been 'No, they can't'.
However, there have been some exceptions shown. Romana chose to regenerate into the likeness of Princess Astra in "Destiny of the Daleks".
The Master chose to regenerate into a younger man in "Utopia".
The Doctor was also able to deliberately regenerate into a 'Warrior' in "The Night of the Doctor", although that was with the help of the Sisterhood of Karn.