Is nature quantized? I was reading Planck's postulate the other day on Wikipedia and couldn't help but noticing the sentence:

"...is the postulate that the energy of oscillators in a black body is
  quantized..."

And a black body is nothing but a theoretic object that absorbs all energy and emits nothing back (i.e. a black hole)
This causes a conflict in my understanding because I know that aside from energy, many other things are also quantized i.e. angular momentum. But I would have never assumed that quantization only exists for a black body.
Can someone resolve this conflict? Is a black body the only thing that exhibits the phenomenon of quantization or is quantization everywhere in nature?
 A: 
Can someone resolve this conflict? Is a black body the only thing that exhibits the phenomenon of quantization or is quantization everywhere in nature?

I am under the impression here that quantization ~ discreteness.
I'll give an example where discreteness pops up in a classical system. Consider a simple stretched string with boundary conditions such that the string has a vanishing amplitude at both ends for all times relevant. Excitation of this string will result in standing waves on the string, which also is the only type of wave such a string will entertain. The thing here is that the frequency specra of allowed oscillations (the standing waves) is of a discrete, or rather quantized, nature.
Is everything quantized? Perhaps. One can argue that any quantum mechanical wave function (modelling some system) experiences some all enclosing boundary conditions to some surrounding such that the only modes of oscillation for the wave function are discrete, in the same sense as the above example with the string. The very basic example would be the 'particle in a box'.
An obvious counter argument would be to consider a wave function of some system which is localized to such degree that the influence of some boundary is negligible, meaning that the wave have not yet ''felt'' the presence of any significant boundary. Though, note the ''yet'' here, since waves tend to spread there ought to always be some kind of quantization due to boundaries however imperfect they are in their rigidness. (Concerning the ''tend to spread'', there is however this phenomenon of Anderson localization, but I feel that's not general enough in scope here).
A: 
Can someone resolve this conflict? Is a black body the only thing that exhibits the phenomenon of quantization or is quantization everywhere in nature?

The black body radiation  which experimentally was inconsistent with the classical calculation of the radiation spectrum forced Planck to postulate quantization. Other phenomena displayed quantization, as the atomic spectra which cam with distinct frequencies. So quantization became a natural consequence in the studies of the microcosm,  which finally led to the development of quantum mechanics, where it appears as the elegant solution of Schrodinger's equation to various boundary conditions.
Depending on the boundary conditions, quantization is rife in the microscopic world of molecules atoms and elementary particles. 
A: It's seems that you are confusing an implication with a biconditional.
Planck's postulate implies that the energy in a blackbody is quantized. Then you say that quantization only applies to a black body. It's like saying if dogs are mammals, then the only mammals are dogs. So if energy in a blackbody is quantized, it doesn't mean that you can't find quantization somewhere else.
Finally, a blackbody is not something that absorbs everything and emmits nothing back. For example, the Sun is quite a good blackbody, see: http://arxiv.org/abs/1010.5696.
A: I would rather turn the question around and ask "Is continuity possible?". In terms of the material reality we inhabit, the answer may well be no, for the same reason that Planck recognized with the black body question, i.e., continuity results in impossible infinities.   
A: Quantization is absolutely everywhere, not just in the abstract thoughts about wave functions and boundary conditions!  In fact as I look around me right now, I don't see anything that isn't quantized. I see rain drops, a dog, my shoe, a table, grains of dirt, an egg, a rug, a car, and so on add infinitum.  After I measure their charge, baryon number, lepton number, angular momentum, or energy, all these objects are in the quantized state corresponding to the quantized variable I measured... at least for an instant of time, until they are bothered by their environment.
All objects around me have an integer(quantized) number of baryons, an integer (quantized) number of charges, a quantized mass, and so on. 
A: Planck derived his postulate particularly for blackbody radiation because that is what he was studying. If energy is quantized as $E=n\hbar\omega=nh\nu$ (depending on your preference), then a bit of work leads to his famous Planck function,
\begin{align}
B_\lambda&=\frac{2hc^2}{\lambda^5}\,\frac{1}{e^{hc/k_BT\lambda}-1}\\
B_\nu&=\frac{2h\nu^3}{c^2}\,\frac{1}{e^{h\nu/k_BT}-1}
\end{align}
The quantum numbers you identify, total, orbital, and spin angular momentum, are for a particle, showing that quantum mechanics is not only for blackbodies.
