I will agree with the comments on the piece kenny posted. More important than the width of the rings is the ratio of latewood to early wood; or darkwood to lightwood. That's what indicates density and strength. I like at least a 2:1 ration. 4:1 is better.
Another factor is where the stave came from relative to the circumference of the tree. A tree that leans will form thick rings on the "downhill side" and thin rings on the "uphill" side. The uphill side is better bow wood provided it has a ratio of 2:1 or better and the rings aren't so thin that you can't chase them. Anything less than 1/32" is a beeotch.
The rings in the center of a log are almost always thick, witness the center piece in Eric's post. They very often are the best bow wood. Young and spry but the diameter complicates things when you want to make a flatbow. Plus pins are more common and cause relatively bigger problems.
You can make selfbows from osage that isn't premium. Just make them wider and longer. Use a whitewood design and you will still make a better bow than you would with whitewood
Dean Torges has some great info in the articles section of his website, particularly on reaction wood:
www.bowyersedge.com