I think it is safe to say that sequels do not have a good reputation. This is for good reason. Usually sequels never match the original movies they follow. Indeed, a lot of times they are far, far worse (just think of Jaws II). Fortunately, Pirates of the Caribbean: Dead Man's Chest is not one of those sequels.
I cannot say that Pirates of the Caribbean: Dead Man's Chest is better than Pirates of the Caribbean: The Curse of he Black Pearl, but it is nearly as good. Like the first Pirates of the Caribbean, Pirates of the Caribbean: Dead Man's Chest blends historical piracy with tidbits of pirate folklore and mythology, while at the same time creating its own mythology. Gore Verbinski's direction is as solid as it was on the first movie. Pirates of the Caribbean: Dead Man's Chest delivers what one wants from a good pirate movie: astounding swordfights, ship to ship battles, colourful characters, and daring escapes. There is even a good deal of comedy thrown in for good measure. I cannot say that there is any sequence that tops the raid that Barbossa's crew made upon Port Royal in the first movie, but there are a few that come close. The first few minutes are particularly impressive.
Of course, like the first movie, much of the film's quality is due to the performance of Johnny Depp as Captain Jack Sparrow. A lot of actors would be tempted to camp it up in a sequel, but Depp doesn't. While Sparrow is still flamboyant, Depp still knows when to rein Sparrow in and be more reserved. Keira Knightley also does a good job as reprising her role as Elizabeth Swann. Indeed, her performance is even more impressive than the one she gave in the first movie. Knightley not only plays the independent, strong willed love interest, but gets to do some fighting in this one as well. Of the leads, only Orlando Bloom seems a bit stiff, but then that seems to he the personality of Will Turner (he was a bit stiff and reserved in the first film as well). Naomie Harris is impressive as the witch woman Tia Dalma.
I do have to warn anyone going to see Pirates of the Caribbean: Dead Man's Chest. It does end in a cliffhanger, and one that is a surprise to boot. Most of the audience I saw it with did not seem to mind, but then I realise that there are those who (for whatever strange reason) don't care much for cliffhangers.
Anyhow, I would recommend Pirates of the Caribbean: Dead Man's Chest to anyone who loved the first movie, loves pirate movies, or just loves any well done movie that is just plain fun.