The Japanese pirate anime One Piece has spawned many one-off movies that, similarly to Dragonball Z, are separated from the timeline of the original series'. These movies are intended simply to deliver condensed plots, large amounts of action and generally engage the audience wanting more, even though not technically considered part of the overall grand story. Given a higher budget from the studio, they therefore have superior animation quality to the show itself.
These are currently only available in Japan or on the net thanks to the generous, hard work of fan-subbers.
One Piece: The Movie - Released in 2000, this movie saw Luffy, Zoro, Nami and Usopp stumble across an island famed for its amazing treasure. It's a very short movie at just under an hour long, but not uncommon in serialized manga movies.
Clockwork Island Adventure - A year later (One Piece movies have been released every year since 2000) the Straw Hat Pirates wind up battling the Trump Pirates after it is alleged that they stole their ship, the Going Merry. This movie also came with a short five minute segment called "Jango's Dance Carnival" which starred the Michael Jackson-esque character from the series.
Chopper's Kingdom on the Island of Strange Animals - When the newest member of the crew, half-man half-reindeer Tony Tony Chopper, gets separated from the rest of the Straw Hats he finds himself declared King by the animals on the island. Also featuring a bonus short "Dream Soccer King!", wherein five minutes of penalty shoot-outs between the Straw Hats and various enemies from the series take place.
Dead End Adventure - Luffy's pirate crew enter an anything-goes water race and come up against a disgraced former Marine with Devil Fruit powers. First movie with new member archaeologist Nico Robin and also the first movie to have a full movie-length runtime.
Curse of the Sacred Sword - Probably the most exciting of all the movies with lots of sword battles, this one involves Zoro, always a man of his word, abandoning his friends and crew to fulfil a promise he made. However, the man he made the promise to has in his possession a sword that has brought upon him an evil curse. The five minute "Take Aim! The Pirate Baseball King!" clip of Luffy's crew facing off against merman Arlong's crew is also included as a bonus. Released in 2004.
Baron Omatsuri and the Secret Island - My favourite of the list, as it attempts to add more emotion and grandeur to the film, more like a Studio Ghibli work. It tells of the Straw Hats responding to a challenge from a mysterious Baron to pit his crew against theirs. Starting similarly to the Davy Back Fight arc in the actual series, the movie takes a turn to darker territories as nakama turn on each other and secrets are revealed
The Great Mechanical Soldier of Karakuri Castle - Luffy battles against Ratchet, the ruler of Mecha Island, to find it's secret treasure. Contains a lot of robotic battles or characters in mech suits a la Neon Genesis Evangelion. Slotting in just before the events of the Water7 arc in the series, it contains some out of sequence events (such as Luffy discovering Gear 2nd before actually discovering it in the series), proving once again why these serialized show's movies tend not to be considered canon.
The Desert Princess and the Pirates - It seems by 2007 the writing team (not Eiichiro Oda, One Piece creator, who continually writes the manga chapters, the core of the series) had run out of original stories. This movie is a "retelling" of the Alabaster saga from the series. An undercover princess recruits the Straw Hats crew's help to defeat a Warlord that intends to destroy her hometown by revolution. The saga was awfully long in the series, so maybe a movie-length version wasn't a bad idea? Not so for the next movie though...
Episode of the Island of Perpetual Winter - Due 2008, this movie is another rehash, this time of the Drum Island story arc from the series. A relatively small part of the saga, this arc told the tale of the people of a snowy island abandoned by it's evil king upon pirate attack, that then have to defend themselves against his homecoming.
So far still under-appreciated in English speaking countries (that is until FUNimation fix up the horrible English dub by 4Kids), One Piece is a great example of a thrilling anime, with its huge worldwide-sweeping adventure storyline, great variety of characters and the perfect balance of humour and action.