Great question. Certainly some of the more gruesome options might be expected. However, it depends very much on the type of pirate that you encountered. Algerian pirates were feared among Europeans because they were known to enslave sailors.

However, some merchant sailors faced entirely different kinds of treatment. A few pirates seem to have used their captives for entertainment. For instance, the narrative of Dutch merchant Lujke Boeckholt (originally published 1741) famously contains an extended account of captured sailors being made to organize themselves into elaborate dance routines. Scholars have long debated the veracity of Boeckholt's account of being forced to act as "dansen dwazen" or "dancing fools" for the pirates' entertainment, as well as passages such as this one: (translation is from scholar Lisa Ekkelkamp's published version of his narrative, 1991)

From there, by their advices, we began to move about the aft of the ship as they shouted commands for us to perform. "Twirl a bit" cried one, brandishing his cutlass "and have the other one gallop as a pony." At that, Heike [an officer on the voyage] did behave as a horse, bouncing with a gallop to the clap of their hands.

After several more exhortations, the pirates (through the medium of a single Dutch-speaker among them) organized their captives into a synchronized 29-step routine accompanied by an unnamed female piratess, who played a crude (and no doubt poorly tuned) analogue to a harpsichord. While this story is far from representative of most captives' encounters with pirates, there are other examples of pirates making use of their captives for their own entertainment. A 1704 London newspaper contains a sensational, and thus perhaps exaggerated or fictionalized, account of a pirate capture off the coast of St. Vincent in which the captives (four men and two young boys) were made to perform the entirety of Hamlet shortly after being captured. (See London Gazette, May 19, 1704)

Finally, and perhaps most bizarrely, conversion narratives during the First Great Awakening in Britain included some accounts of former pirates describing their sins. One convert, named Pete Cooke, described his amusement in his past life at forcing the captives to play, at pain of death, a game of his devising that he called "Fowle, Fowle, Swine" (qualitatively similar to the children's game "Duck, Duck, Goose" of today).

References:

Brian Gillen, Antics over Anchor (2007)

Gregory Lipsky, Rituals of Humiliation in Atlantic Pirate Culture (1994)

EDIT: This is an April Fools' answer, and should not be taken seriously.