You likely remember from your early school studies that Queen Elizabeth I was a patron of Sir Francis Drake who commanded the Golden Hind and was not only an explorer but also a privateer – a pirate with a noble title. Then there was Blackbeard, Captain Edward Teach (or Thatch), who during the reign of Queen Anne was a pirate in what was then called the West Indies. Pirating in the Mediterranean, we had the Barbarossa brothers who hailed from the island of Lesbos; Barbarossa means Redbeard, of course. I do not know the name(s) of their ship(s).
In Robert Louis Stevenson’s Treasure Island, the lowly, one-legged cook aboard the pirate ship Hispaniola goes by the name Long John Siver and is head of the pirates. According to what I read today, Treasure Island introduced many of the pirate story tropes that are popular today: one-legged pirates, the pirate’s companion parrot, treasure maps, and so forth. Disney, of course has the Pirates of the Caribbean and Jack Sparrow who captains the Black Pearl. Then there is Captain Hook, a character in Peter Pan, whose fictional ship is the Jolly Roger (also the name of a nuclear missile in the SciFi movie Independence Day).
At this point, you have already concluded that I am naming famous pirates, both historical and fictional, because today is International Talk Like a Pirate Day. See the origin of this odd day here.
Other renown captains who were not pirates include Captain James Cook who commanded the HMS Endeavor whose voyages of exploration in the Pacific included the mapping of Australia, New Zealand and Hawaii. There was also Captain Robert FitzRoy (later Vice-Admiral) who was captain on the second voyage of the HMS Beagle that took a young Charles Darwin on a journey that gave us the foundations of the Theory of Evolution.
I am sure that you can think of many others as famous and a few notorious as well. All I can say now is, Arrgh!