Henry Morgan, though technically a privateer rather than a pirate, was the Pirate King. He became an Admiral, was knighted and commanded a fleet of bucaneers throughout the Spanish Main. The only Pirate, in western culture at least, who can mount any reasonable challenge to his success is Black Bart Roberts.
Morgan's speciality was attacks on locations rather than attacks at sea. He sacked Puerto Principe, he became the first man to successfully capture the port of Porto Bello - which the Spanish thought impregnible at the time - he raided Maracaibo and sacked Gibraltar and destroyed two Spanish ships on the way out while taking the third for himself, then finally was his great raid on Panama where he defeated the forces there in open battle and failing to find the wealth he wanted he burned the settlement to the ground.
By the time of his retirement, Morgan was the most feared bucaneer in the Spanish Main and he had become an English celebrity, being one of the few success stories in Englands recent war's with Spain.
He was a great charismatic leader, capable of drawing men to him and keeping the many different pirates, privateers and bucaneers in the Spanish Main united, but he was a self-serving man who was fully prepared to abandon his allies to keep most of the wealth of his exploits for himself and a few loyal men - indeed it was this trait that led a former friend to write a libelous and largely fictional account of Morgan's exploits in an attempt to destroy Morgan's reputation.
He also didn't have the best of luck with flagships. He lost three. The Oxford was destroyed when some fool set fire to the magazine after getting drunk during a party, the Satisfaction hit a rock off the caribbean coast of Panama and the Jamaca Merchant hit a reef off the coast of the Isle a vache