Sometimes your mind tends to exaggerate what you see through the viewfinder of your camera. You often perceive things to be bigger than they actually are and you also tend not to notice 'slight' distractions. What you end up with is photographs with huge areas of wasted space around the edge.
My favorite way to fill in space is with macrophotography and I have a load of fun with it.
Most cameras have a macro mode (also called close-focus) that lets you get a sharp focus within just a few inches of the subject. When you get that close, especially if you zoom in, you can get very cool results.
Most cameras don't automatically close-focus. Instead, you need to activate that setting by pressing a button on the camera body. Most manufacturers use the familiar tulip symbol to indicate macro mode--look on the camera body, or perhaps on the LCD menu system, for this symbol. Remember, though: When you're done shooting your close-ups, turn off the macro mode or your normal photos will be blurry. Macro focusing works only when you're within a few inches of the subject.
Here are a few of the macros I've done by using the macro setting (on most cameras marked with a little tulip icon) on my Sony DSC H1. I love how it makes things noticeable and gives you a totally different prospective. (click the titles)
Little toad family
Have fun playing with the macro setting, play a lot! With digital, you aren't wasting film, or paying for prints unless you like the results and I think you'll find that you'll like many of them.