This is a thought I started playing with years ago, but a recent exchange with Dennis Markuze brought it back to mind. So, I thought I'd write it down while it was fresh in my thoughts again.
Curses and prophecies are, in some ways, two sides of the same coin. They're both statements about the future, and they both assume that the future is - or can be - fixed and static. The difference is that a prophecy predicts future events, while a curse (at least ostensibly) causes or shapes future events.
Mainly, this is something to consider when writing High Fantasy (which often includes prophecies as a means of foreshadowing or even pushing the plot along), or Horror (where, if you're going to employ or imply a curse, it helps to know how such a thing might work - for example, does saying it cause the victim to arrange the result, or is there some outside force nudging events towards the desired end?). It's also interesting as an element in mythology, where in some cases - the story of Oedipus is a classic example - it's hard to tell the difference between the two.
In the real world, of course, the future is fluid. (Either that, or it seems that way to us, which amounts to the same thing.) We can make predictions, but we can't speak with certain knowledge of events that have not happened yet.* Prophecies in the real world fall into one of two categories: either they're so vague as to be effectively meaningless, or they're easily falsified.
* Hell, we often have trouble speaking with certain knowledge of events that have already happened. There are two sides, at least, to every story; and eye witness testimony is among the least reliable.