Jack's sword is a hanger (a 17th and 18th century style of sabre), rather than a cutlass, the weapon preferred by most cinematic pirates. The sabre's longer blade allows him to keep his enemies a few inches further away than a cutlass.
Jack's pistol changes from film to film. In The Curse of the Black Pearl, Jack carries a single barreled pistol that was given to him when his crew deserted him after their mutiny. In that film, he never used the pistol because he was saving his only shot to kill Captain Barbosa. In Dead man's Chest, it is shown in his escape from the turkish prison that he carries a double-barreled pistol with him.
After his compass, Jack's most prized possession is his hat. He is rarely seen without it, and he always mentions it when discussing his effects. When Jack orders the ship to head for land to escape the Kraken, his hat is tossed overboard by Jack the monkey. A panicked Sparrow commands it be left behind, which so surprises the crew they are literally struck motionless. The hat, which is picked up by nearby Turkish fishermen, is eaten by the Kraken when it attacks the wrong ship. Jack spends the entire film searching for a suitable replacement and even walks through a pub fight trying on the brawlers' tricornes. He eventually regains his own hat when it is regurgitated by the Kraken as is about to devour him. Covered in mucus, Jack merely shakes it off and puts it back on before drawing his sabre and attacking the monster.
Captain Jack's compass, obtained in a barter with Tia Dalma (as established in Dead Man's Chest) is charmed, or perhaps cursed, it is not made plain which applies. Its needle points to whatever the person holding it wants most, rather than pointing towards north. Often pointing towards a treasure or other valuable items, though it might instead also point towards a person or a geographical location. It works for anyone using it, but is only of use to them if they are aware of what it is that they truly want. It will even work while lying untouched on the ground, if the possessor is nearby. When it fails to work properly for Jack, Tia explains that it is because he does not know what he truly wants, "or do you know but are loath to claim it as your own".
When Captain Jack Sparrow is arrested after saving Elizabeth Swann from drowning (in the first "Pirates" movie), Commodore Norrington searches through his possessions. Most of what he finds appears to be junk, including a compass that does not point north. In fact, north, south, east, and west are not even specified on it.
Later, a hint of the compass' true nature is revealed. When Will notices Jack using the odd instrument to navigate through a storm, he asks Gibbs how they're supposed to find Isla de Muerta with a compass that doesn't work. Gibbs replies, "The compass doesn't point north. But we're not trying to find north, are we?" The compass points them to the island.
When, in the second film, Elizabeth learns that Lord Cutler Beckett wants Jack Sparrow's compass, she mistakenly believes he is searching for the treasure on Isla de Muerta and warns him about the cursed Aztec gold. However, Beckett says that the compass does not only point to Isla de Muerta and that there are "other chests of value in the sea."
During the Kraken's attack, Jack deserts the Black Pearl and his shipmates in a longboat. He pauses a moment to look at his compass. Although it is not shown where the needle points, he returns to the ship and saves his crew.