The Ouroboros tattoo was the trademark insignia of the Corsair. It depicted a snake eating its own tail, representing Eternity. The Corsair got it inked on their body in a different place each time after regenerating. (TV: The Doctor's Wife, PROSE: Eleven Things You Probably Didn't Know About the Corsair) The Eleventh Doctor said the Corsair "didn't feel like himself... or herself" without the tattoo. (TV: The Doctor's Wife)
Instances of the tattoo
The Third Corsair had the largest tattoo, being multicoloured and spanning their entire back. The Fifth Corsair had the smallest, the size of a ten pence piece on her upper thigh. (PROSE: Eleven Things You Probably Didn't Know About the Corsair) The Sixth Corsair had it inked on top of her left wrist. (COMIC: Old Friends) The Ninth Corsair had it on his inner left wrist. (PROSE: One Virtue, and a Thousand Crimes, TV: The Doctor's Wife) The Eleventh Doctor recognized that after being killed, his arm was used by House to create Auntie by seeing the tattoo. (TV: The Doctor's Wife)
Other incarnations featured the tattoo on the back of their neck, once again on their inner left wrist, on their upper back, their outer right wrist, the back of their left hand, and the side of their right thigh just above the knee. (PROSE: Eleven Things You Probably Didn't Know About the Corsair)