The Pink Panther
The first film is much simpler in tone and narrative than the others, and is considered by many to be a comedy classic. It introduced the protagonist, Sir Charles, with Clouseau as a secondary character, and took place mostly at a ski resort where Clouseau is trying to prevent the theft of the Pink Panther diamond, unaware that his wife is Charles' partner-in-crime.
A Shot in the Dark
The second film has no relationship to the first other than Clouseau, and the Pink Panther motif is dropped due to the plot not featuring the diamond. Sir Charles, the intended protagonist of the series, does not appear, and the Pink Panther in the title sequence is replaced with an anthropomorhpic bullet. The film deals with several murders in a mansion where all evidence points to the maid but Clouseau, who is in love with her, fights to defend her. Many consider this to be better than the first film, and it established many of the recurring elements and chartacters of the series.
The third Clouseau adventure was made independently and features no regular characters other than Clouseau. Clouseau was also played by Alan Arkin, instead of the regular Peter Sellers. This is not strictly speaking a Pink Panther film as the title would only return to the films with the next one.
Return of the Pink Panther
Recurring characters from the first two movies return in this down-the-line sequel to the first movie. The Pink Panther returns to the plot and the title, and from now on would continue to appear in the title and title sequence whether it was involved in the plot or not. Sir Charles returns with both him and Clouseau as protagonists- but from now on Charles would be a minor recurring character with Clouseau having taken over as the main character.
The Pink Panther Strikes Again
Considered by many to be the greatest film in the series, this entry sends up science fiction and horror tropes with recurring villain Dreyfus ascending to main villain, blackmailing the world into killing Clouseau using a doomsday device. Interestingly, Dreyfus would return in his saner form in all subsequent films and would no longer play a villainous role. The over-the-top plot and crazy gags are balanced out with interesting character development for Clouseau, as he attempts to solve the mystery of how this came to be, and avoids being killed by every government in the world.
Revenge of the Pink Panther
The next entry in the series has the ending of the previous film somewhat undone, leaving some speculation that it could be an alternative follow-up to Return of the Pink Panther. With more gags, disguises and slapstick action than ever, the film still follows a more realistic plot: Clouseau is believed killed, and, secretly alive, tracks down the Mafia man that had it arranged. This is the first of a trilogy of films dealing with the French Connection. It would also be Sellers' last. The planned follow-up film, Romance of the Pink Panther never happened but the series still continued with the rest of the regular cast.
Trail of the Pink Panther
In a film that resulted in a law-suit, Sellers returns as Clouseau, albeit with deleted scenes from The Pink Panther Strikes Again being used. For the first time since Return of the Pink Panther the titular diamond returns to the plot as both the diamond and Clouseau go missing. In a tribute to the series so far, the heroine of the film, Marie Jouvet, interviews the other characters on their experiences of Clouseau, whom they all are certain is very much alive, while the Mafia tries to prevent Clouseau from being found.
Curse of the Pink Panther
A direct sequel to the previous film, the hero this time around is Clifton Sleigh, the man who has been hired to find Clouseau and the diamond, and is an idiot thanks to Dreyfus ensuring that a man who could actually find Clouseau can't be used. This is the last film to feature the Mafia in the plot, and features Roger Moore in a cameo as Clouseau. The other characters from the series so far appear as well.
Son of the Pink Panther
With the idea of Clifton Sleigh returning having been dropped, this last film breaks away from the Pink Panther diamond\Clouseau plot, which was resolved in the previous film, to focus instead on the exploits of Clouseau's son, Jaques Gambrelli. For the first and only time throughout the entire series, Clouseau does not appear. The old friends make their final appearance as well, as Blake Edwards died before the series could be continued (although he had possible plans for more films featuring Clouseau Jr.) but their stories are tied up nicely.
The Pink Panther
The first film in the series not to be made by Blake Edwards, and to feature an entirely new cast, this recent reboot of the series featured Clouseau as the hero again, with some of the old characters and the Pink Panther diamond. Instead of rebooting the story completely, they decided to make it a prequel to the other films, dealing with Clouseau's backstory (despite the setting being, of course, modern).
The Pink Panther 2
The last film in the series is the sequel to the prequel, as it were. The cast from the previous film returns, and there has been talk of a third film in the new series.