I also have to add the importance of building stamina, not to mention strength. One of my (ballet) teachers used to have me run up and down the steps of my high school gym and he used to also have us do wall push-ups. These are done in a hand-stand position but up against a wall for balance and with one leg bent so you can keep your back straight and not arch.
He (and we) found that these wall push-ups were great for building overall back strength. (Just think of all of the lifts and partnering men need to do.)