I threw together some quick references for the different POTC movies while I was going through them earlier, maybe handy for someone else, the main elements of each...

Pirates Of The Caribbean 1 - The Curse of the Black Pearl (2003)
Character introductions, the unlucky captain Jack, Bill the swordsmith and Elisabeth the lady. Barbosa, The Black Pearl, a cursed treasure and pirates versus cavalry. Also the most memorable escapes from the gallows and the underwater skeleton army scene.

Pirates Of The Caribbean 2 - Dead Man's Chest (2006)
Sparrow's debt to Davy Jones, The Flying Dutchman, Bill's father, a new villain of state, a strange fortune-teller lady and fate... ends with the Kraken.

Pirates Of The Caribbean 3 - At World's End (2007)
A journey to the end of the world in search for Jack, followed by a disappointing gathering and showdown between all pirate brethren and a great armada, and the goddess Calypso who contributes a decisive maelstrom. Stone crabs intro. Whatever happened to the Kraken?

Pirates Of The Caribbean 4 - On Stranger Tides (2011)
The fountain of youth. Sparrow, Blackbeard, Barbosa, England, Spain, mermaids, jungle scenes, the wheel duel, and an old female acquaintance who seems a little crazy. Very different from the previous three.

Pirates Of The Caribbean 5 - Dead Men Tell No Tales (2017)
Poseidon, captain Salazar, Barbosa's daughter, the compass, and an end of all curses. Bill and Elisabeth are back too, and their story concludes.

The first three could be seen as part of the same saga - where movies two and three are basically two parts of the same movie split up, the fourth a spin-off (few re-occurring characters), and the fifth one more of a return to both the cast and story of the original three, as well as a conclusion to all.

The first one's definitely the best one - only one that truly stands on its own.