It’s worth pointing out that I’m showing you one way that I’ve created wood shaders, but the Cycles nodes are so flexible that there are often many ways to accomplish the same thing.  For example, in the first post in the Procedural Wood series (The Beginning), I showed how to create rings based on the x^2 + y^2 = r^2 equation of a circle. However, there are definitely other ways to get something resembling rings. For example, there is even a “Ring” pattern for the Wave texture. If you just remove the Y-component of the Vector as we’ve done in previous posts:
rings01-01
…you get a nice pattern for a lot fewer nodes:
rings01-02
It’s probably hard to find a faster way to get rings! Another way is to use the Color output of the Normalize Vector node, like this:
rings01-03
…and this is the resulting ring pattern:
rings01-04
I encourage you to experiment with different nodes and see what kind of effects you can get. In my opinion, neither of these two methods are as easy to manipulate as the Circle Equation method we explored before. However, depending on the particular look you want to create, these might work better for you.

If you find more methods, I’d love to hear about them!