Probably the most important compositional rule you can learn (and probably the one I should have mentioned first! D'oh as my son would say) is to fill the frame.
Photography is a subtractive process, as opposed to something like painting which is an additive process. With a painting you gradually add things to a blank canvas. With photography you start off with a canvas that has way too much stuff in it and you have to crop out the unwanted so that all is left is the subject of your picture.
The famous photographer Robert Capa once said that if you don't like your photos get closer. Part of the photographic process is to really think about what it is you're photographing before you press the shutter. And then to get rid of everything else in the frame that isn't what you're photographing. If you can list four or five things that you want to put in the picture chances are you've got too many. Narrow it down to one, two or three at the very most.
But we don't all own $10,000 1200mm telephoto lenses and sometimes we can't get close enough to fill the frame, and sometimes we don't want to use a telephoto but want a wider view.
Take this picture here. This is the night view looking out over Hakodate, Hokkaido, Japan. From where the lookout was I could get a great view looking along the coast of the peninsula. I tried a couple of long telephoto shots concentrating on certain areas but I wanted a wider shot which showed the long stretch of coastline.
The only problem was when I did that I suddenly had a big black patch in the bottom of the frame where the mountain got in the way (what idiot put a mountain there anyway! :) ). I needed to fill that black with something. And then that something came along in the shape of a bus. I could see it moving up the mountain quite slowly and just sat there and waited until it came around the bend. A slow shutter speed ensured that you got the streaking lights, and it being a curved road means you get a nice shape and voila I've filled my frame with city skyline, and my blackness with bus lights.
Take a look at the photos you really admire and look at how the photographer has filled the frame and what with. Sometimes they deliberately walk up to something to get closer, or zoom into it. That's a really great way of ensuring you fill the frame. Or sometimes they have sat and waited until something has come into the frame to fill a blank part of a wide-angle shot. Either way works.