One of the biggest issues I come across when I watch other photographer's shoot is watching them trying to capture a perfectly composed image. I'm not saying you shouldn't try to compose your shots perfectly (You really should), but you need to think twice about what you are shooting for. Are you planning on printing your photo or are you only going to be showing it off digitally?
If you are printing your shots, you want all the pixels you can get. The higher the resolution, the bigger the print can be. For most photographers you'll want to show off your work digitally. Since that's the only way I show off my shots, every image has been resized to have it's largest length be 1500px. My camera shoots at an image resolution of 4,928 x 3,280. That gives me two options: I can resize the full, properly composed image to 1500px or I can take any section of the image down to 1500px and use that.
Here's an example of what I mean...
The overall image is the full resolution from my camera. That small white box is 1500px wide and is all I am showing off on my site and Facebook. That means there is no difference between shrinking the entire image down to that white box size or just cropping a section that small of any image I take.
Why am I bringing this up? Many images I have taken in the past have ok composition that I know could have be easily improved if I was a little closer. Well, since I only need 1500px of the image, I just crop in until I am happy with it. Look back at the photos you have taken. I am sure there are some you can play around with that you weren't happy with before.