The most famous case of this occurring is probably the Amistad. Africans that had been captured and enslaved in West Africa were transported by ship to Havana, and purchased at auction. When they were being moved a second time to another part of Cuba, one of the enslaved was able to free himself, free the rest of the enslaved, and start a mutiny that led to the deaths of all of the non-enslaved on the boat with the exception of the two owners of the boat, who were kept alive to navigate. The enslaved demanded to be returned to Africa, and used the sun to determine whether or not they were heading in the correct direction.

However, the two owners of the boat secretly navigated back West after sundown each day, trying to return to territories where slavery was legal in an effort to save their own skins. Eventually, after a 63-day journey, they landed at Montauk Point, at the far eastern edge of Long Island.

At that point, the US government classified the slaves as “stolen property” (they stole themselves?!) and were charged with piracy and murder.

There is quite a story from that point - the case moved its way through the US court system before making its way to the Supreme Court, the ultimate outcome of which was that the slaves were ruled free men and sailed back to Africa on a ship named the “Gentleman”.

So, there’s at least one case where after a long and arduous journey, the slaves secured their freedom and returned to their homeland. There’s a pretty good movie about it directed by Steven Spielberg - recommended!

Source: The Amistad Rebellion, Marcus Rediker

So in addition to /u/DCLutz77's response on the Amistad, I'd like to talk to share events the Clare back in 1729.

Here's a summary from Marcus Rediker's Outlaws of the Atlantic (2016) [repackaged from his own The Slave Ship: a Human History (2006)] :

Insurrections aboard slave ships usually had one of four outcomes. The first of these was exemplified in 1729 aboard the Clare galley. Only ten leagues out to sea off the Gold Coast, the enslaved "rose and making themselves Masters of the Gunpowder and Fire Arms," drove the captain and crew into the longboat to escape their wrath and took control of the ship. It is not clear whether the successful rebels sailed the vessel or simply let it drift toward the shore, but in any case they made landfall and their escape to freedom not far from Cape Coast Castle.

Rediker is quoting from The Boston News Letter of Sept 25, 1729:

The Clare... having completed her Number of Negroes had taken her Departure from the Coast of Guinea for South Carolina; but was not got 10 Leagues on her Way, before the Negroes rose and making themselves Masters of the Gunpowder and Fire Arms, the Captain and Ship Crew took to their Long Boat, and got shore near Cape Coast Castle. The Negroes run the Ship on Shore within a few Leagues of the said Castle, and made their Escape.

Sadly, that's about all we can expect from the news that would have been reported for these events back in the day. But Rediker goes on to tell another story you might be interested in:

An even more dramatic rising occurred off the Wind-ward Coast in 1749. The enslaved picked the locks of their shackles, grabbed large billets of wood off the deck, fought the crew, and after two hours overpowered them, forcing them to retreat to the captain's cabin and lock themselves inside. The following day, as the captives ripped open the quarterdeck, five members of the crew jumped over-board in an attempt to escape but discovered the hard way that some among the captives knew how to use firearms; they were shot and killed in the water. The successful insurrectionists then ordered the rest of the crew to surrender, threatening to blow up the powder room if they refused. The vessel soon ran aground, and before leaving the victors plundered it. Some of them went ashore, not in the naked-ness required on the ship, but now clad in the clothes of the crew.

... this story is (according to the footnotes) sourced from the 18 Dec 1749 edition of The Bath Journal, but sadly the BNA doesn't have that issue available online.

Hopefully this gives a taste of some other, less known slave mutinies.

In addition to the cases of the Amistad and the Clare brought up by u/DCLutz77 and u/rmosquito, another ‘almost’ example is the mutiny on the Creole, which was entirely successful, though not trans-Atlantic.

In 1841, the same year as the slaves from the Amistad were freed by the Supreme Court (two years after the Amistad mutiny itself), the trans-Atlantic slave trade was illegal in most relevant countries: the Danish, British, Dutch, French, Spanish and Portuguese empires from 1792, 1807, 1818, 1820, 1826 and 1836 respectively, with their successors inheriting that, and the U.S. from 1808 and Haiti from its foundation.

The Creole was a ship transporting slaves from Richmond, Virginia to New Orleans.

Madison Washington was himself a formerly escaped slave who had fled to Canada via the Underground Railroad, and like the more famous Harriet Tubman had returned to free his loved ones as well (in this case his wife), but unlike Tubman was unfortunately recaptured and transported on the Creole.

A crew member left a grating open where he and others had been held. He reached the deck with several others and killed one of the crew - one of the slaves was also killed in the resulting fight, but the slaves managed to commandeer the ship.

At the suggestion of one of their number, Ben Blacksmith, they forced their overseer to navigate the ship to Nassau in the Bahamas, since they were under British rule and slavery had been abolished in the British Empire since 1834.

This caused a stir in Nassau, where the black harbour pilot informed them they were free. There was a fight instigated by the American consul in Nassau to put control of the ship back in American hands but it was unsuccessful.

The nineteen mutineers were arrested for mutiny and then set free on the grounds they had the right to fight their captors as free men. The rest were free immediately.

The U.S. Secretary of State, Daniel Webster, lodged a formal complaint with the British government and demanded the return of the slaves. This also did not succeed. Congressional debates based on the abolitionists’ position that slavery was already illegal on the high seas led to the U.S. and UK signing the Webster-Ashburton treaty, where the U.S. agreed to abolish the ‘coastwise’ slave trade as well.

There is also the story of Robert Smalls, another slave who was in fact employed (or ‘used’) by the Confederacy to steer the CSS Planter around the coast of South Carolina (under the supervision of a white captain he got to know well). He asked his commander to allow the families of those enslaved on the ship to visit, which he agreed to. The families pretended to go home for the evening but hid. He disguised himself as the captain (with a straw hat covering his head, making use of the dark of night), and, using the correct codes, simply sailed to the U.S. ships further out that were blockading the South, and handed the ship over to the Union. He later became a U.S. representative for South Carolina during Reconstruction.

One good reference for the Creole case: Hendrick and Henrdick, The Creole Mutiny: A Tale of Revolt Aboard a Slave Ship