Most rigid materials Ordinary web searches are not turning up lists of the most rigid materials for me.
I am interesting in finding out the relative rigidity of commonly available materials and how to measure that rigidity (Young's Modulus?)
Some of the rigid materials I can think of are (1) hardened steel, like 4140 or tool steels, (2) silica, (3) granite, (4) basalt, (5) boron nitride, (6) tungsten carbide
How can I compare materials like this to determine their relative rigidity?
 A: You probably know Hooke's law: the force $F$ to modify the length of a spring by $d$ is $F = kd $, where $k$ is a constant factor characteristic of the spring (sometimes called "stiffness"). Springs with different geometries (but made of the same material) can have very different $k$.
You are looking for an "intensive" quantity that is a pure property of the material only.  The different "elastic moduli" (bulk modulus, shear modulus, Young modulus...) are properties of the material analogous to the spring's stiffness (i.e. they tell you the response of the material to some applied stress) but do not depend on the geometry of the body and its boundary conditions (namely, they are local properties valid for an homogeneous and small "material element"). There is no direct relation between stiffness $k$ and the elastic moduli, as geometry and boundary conditions can be complex. However, keeping constant the geometry of the body, it is reasonable to expect that recaling the elastic modulus of the material by a factor close to unity (i.e. changing the material with another one of similar modulus), the stiffenss of the body changes by the same factor.
Similarly to $k$, that can be defined as the slope of the force-deformation curve, the elastic modulus is the slope of the stress-strain curve in the linear regime, namely when the strain is small enough that the material response to the stress is linear (similarly to Hooke's law, that is valid for small $d$).
Both the stress and the Young modulus have the physical dimension of a pressure (the strain is dimensionless!). As suggested in the comments, the highest known Young's modulus value is that of diamond (~ $1.2 \times 10^{12}$ Pa).
A: In engineering terms, you want to compare the modulus of elasticity of various materials. Engineering handbooks on the properties of materials and college textbooks on materials science  will list those moduli in tables for you.
