This video contains a quick, upper body training circuit using Olympic rings. Try some (or all) of these for yourself and see the difference ring training can make.
One of the benefits of ring training is that it requires a greatly increased amount of muscular control to stabilize the body, especially in the pressing ranges, resulting in a high degree of muscle fiber activation. Another great benefit is that you can easily modify most of the exercises, simply by adjusting your body position. In many cases, you don't even need to adjust the length of the rings.
For clarification on that, lets use the Ring Push Up as an example. The more horizontal your body is the harder it will be. The more vertical you stand, the easier it becomes, because you're resisting against a lesser percentage of your body weight. The same is true for other pressing exercises, rows, curls, extensions, flys, etc.