Ye can't beat the original. Though each movie has special qualities that I like, for instance; I watch POTC2 for the humor. Jack and the cannibals always leaves me in a hysterical laughter.
I also thourougly enjoy the kraken scenes. The music and animation is phenomenal.
POTC3 is definitely a darker, more intense plot. Though it can get a little out there
I enjoy the story line it follows. For instance, the Brethren Court was a nice addition to the plot in my opinion.
Other scenes such as the battle between the Dutchman and the Pearl are also really quite amazing.
Each movie captures my eye in a different way, for different reasons. And though it is hard to choose amongst the three, I still have to give the title of 'favorite' to the first, Pirates of the Caribbean:
Curse of the Black Pearl. It truly captures the general sense of a 'pirate' in all its originality. It stays on topic, within the Caribbean, and really holds true to what we today think of as 'pirate-like'.
The first movie also gives us the best sense of the characters as well. For instance, I feel Jack, though witty throughout the trilogy, has many of his best moments and most memorable lines in the first movie.
As they say, 'There is nothing like the original.'