Pirates and Monkeys
It'll probably never be clear whether or not Monkey Island acted as a direct influence on the Pirates of the Caribbean trilogy, though given the similarities, it seems at least fairly likely. Of course, it's worth remembering how much of the original Secret of Monkey Island was taken from Tim Powers' on Stranger Tides.
Given the sheer volume of differences in both plot and character development alongside the (if we're honest) relatively scant comparisons, it's probably fairer to say that Pirates of the Caribbean was, more than likely, influenced by the Monkey Island series, though not in the unseemly fashion that so many avid gamers seem to believe.
Regardless, Pirates of the Caribbean has whetted a seaborne appetite, and we wait in hope for some confirmation of the long-rumoured fifth entry in the Monkey Island series. Hopefully we might even be lucky enough to discover just what the Secret of Monkey Island really is.