The very first thing books about photography tell everyone is about the Rule of Thirds. It's actually very simple but until I knew about it, it never once occurred to me to do it.
Imagine a tic-tac-toe board on your viewfinder (actually, many cameras now offer you the option of putting that 3x3 grid right on there for you). It isn't there for you to use to help center your photo (though you can use it that way if you truly want something dead center). The trick is to use the intersections of the lines.
When you put something of interest at the intersection of one of the crossed lines, it adds interest to the photo. I have no idea how this works but it does. Of course when composing your shot you also take into consideration the rest of the elements but if you can put a bright spot in one of those intersections, you'll be much more likely to have a more interesting composition.