Like Jason Kottke, the first paragraph of Dana Stevens' review of Pirates of the Caribbean: At World's End (which contains a lot of spoilers) does an excellent job of explaining the film's appeal to me:

With Pirates of the Caribbean: At World's End, the summer blockbuster begins to approach the level of pure abstraction. Adrift in the windless seas of its 168-minute running time, the viewer passes through confusion and boredom into a state of Buddhist passivity. Swords are crossed, swashes buckled, curses lifted only to descend again. People marry, die, come back to life, transform willy-nilly into barnacle-encrusted ghouls. There are reasons why all this is happening, reasons that might be clear if you've recently pored over the previous 294 minutes of pirate lore. Like all abstract art, At World's End is best approached non-narratively, as an experience rather than a story.

Amazing visuals and editing (the marriage scene was nice). Good acting by Johnny Depp and especially Bill Nighy. A nearly incomprehensible plot.

Although I am not giving Gore Verbinski et al the benefit of the doubt regarding whether this was an intentional effect, the film reminded me of movies like Dead Man by Jim Jarmusch (and, coincidentally I am sure, also starring Johnny Depp). It's a stream of imagery and scenes, dream-like by their lack of logical structure and cohesiveness, that you experience rather than try to understand. To me, one of the most defining qualities of dreams is how aspects of reality can change drastically from one moment to the next - I am in the house I grew up in, only suddenly that house is in the U.S., etc. Pirates 2 and 3 are similar, and while on the one hand it is nice once you accept it (and I agree with Mr. Kottke that an early surreal scene helps set the tone), I kept wishing the writers had created a coherent plot structure (rules of the world, characters, etc.) Ah well, it was fun to watch, more than most senseless summer blockbusters.