I watched the entire trilogy over a few days earlier this year, and the sequels indeed make a token amount of sense when you actually pay attention. The films are not non-stop action (there are really only a couple major action sequences in each sequel), they do not make the mistake of explicitly centering on Jack Sparrow (the Han Solo/Donkey of the series). And while it annoyed me upon initial viewing, I now admire the fact that you're actually rooting against Jack Sparrow for much of Dead Man's Chest, since his plans are specifically preventing Will Turner (a vastly underrated Orlando Bloom) and Elizabeth Swan (Keira Knightley, who is really the lead character of the whole series) from having their happy ending.
Weirdly enough, the trilogy on the whole eventually becomes a relatively powerful metaphor for America's moral compass in the 'War on Terror' era. To put it somewhat simplistically, in the first film, the British government is virtuous and the pirates and the clear-cut bad guys. But over the course of the sequels, evil corporate interests hijack government, and said government so overacts to the (comparative) nuisance of piracy that they are the villains by the time the series reaches its conclusion. Heck, by the start of At World's End, the formally righteous British government troops are hanging children and murdering elected officials.
Anyway, political parables aside, the Pirates of the Caribbean trilogy remains a thoroughly satisfying bit of popcorn entertainment, proudly over-plotted and arguably too clever for its own good. But Gore Verbinski's epic trilogy (written by Ted Elliott and Terry Rossio) is an inarguably ambitious achievement that should not be discounted because it runs a little long and dares (like The Dark Knight) to challenge the moral purity of the first film. Rob Marshall indeed has something to live up to, and I sincerely hope he doesn't cop out and deliver a safe, inoffensive pirate movie. Verbinski certainly delivered far more than that three times in a row.