Here's a little exercise I've been doing lately that I'm really enjoying. Take an image that you really like (painting, illustration, photograph, movie still, whatever) and do a little thumbnail size study. Don't worry about the details, that's why you're working so small. The idea is to get past the content of the picture and see the underlying composition: lights and darks, warms and cools, the big puzzle pieces.
Here are a few of my examples:
These are digital greyscale, originals on the left and my studies on the right. You can click for a slightly larger view, but really the point is to see things small so you get away from the details. The pictures are from my favorite book: Tales from Outer Suburbia by Shaun Tan.
Here are a few from famous paintings - 10 points if you can name them all. I wanted to try a few outside of the computer, so I did most of these using my fountain pen. I also tried a few in gouache so I could study the color arrangements.
These are a few modern works. From the top left: Chris Van Allsburg, Gianni De Conno, Shaun Tan again, a photo from my favorite photographer Lartigue (look him up, he has a very interesting story), Eric Fortune, Jens Claessens, Shaun Tan again again, and Peter Nguyen.
This is a good way to deconstruct works of art you like and see what makes them so appealing. It's also a good way to rehearse successes, get a feeling for what makes a composition work so that you can apply those lessons to your own work.