Why don't extraordinary rays follow Snell's law? I understand that ordinary ray (O-ray) and extra-ordinary ray (e-ray) have different refractive indices.
This should mean O-ray and e-ray move with different velocities in a substance and they should refract at different angle according to Snell's law.
If the angle of incidence is zero, the angle of refraction should also be zero, i.e a ray would move undeviated if the angle of incidence is zero.
However, I have seen that e-ray bends even if the angle of incidence is zero (which means e-rays don't obey Snell's law).
Why this is the case?
 A: The distinction between "ordinary" and "extraordinary" rays arises when you have a birefringent material, in which light with different polarizations has different speed.
Snell's Law, like many "laws" in physics, is not an absolute description of all behavior but a mathematical shortcut based on a more fundamental description which applies in many common circumstances.  You can derive Snell's Law, for light traveling from a medium with permittivity and permeability $\epsilon,\mu = \epsilon_1,\mu_1$ to a medium with $\epsilon_2,\mu_2$, by demanding that the following boundary conditions are satisfied:
\begin{align}
\epsilon_1 \vec E{}_1^\perp &= \epsilon_2 \vec E{}_2^\perp
&
\vec B{}_1^\perp &= \vec B{}_2^\perp
& \text{normal to surface}
\\
\vec E{}_1^\parallel &= \vec E{}_2^\parallel
&
\frac 1{\mu_1} \vec B{}_1^\parallel &= \frac 1{\mu_2} \vec B{}_2^\parallel
& \text{parallel to surface}
\end{align}
Here the superscripts $^\perp$ and $^\parallel$ indicate orientation with respect to the surface, not to any polarization axis.  The external wave will have the form
$$
\vec E_1 = 
\vec E_A \exp i\left(\vec k_1\cdot \vec x - \omega t \right)
+
\vec E_B \exp i\left(\vec k_1\cdot \vec x - \omega t \right)
$$
where $\vec E_A$ and $\vec E_B$, representing the two plane polarization components of the incident wave,  are orthogonal to each other and to the wavevector $\vec k_1$. The magnetic field $\vec B_1$ is orthogonal to $\vec E_1$ and to $\vec k_1$.
The details of the derivation can be found in many E&M and optics textbooks.
In a birefringent material you have the complication that the permittivity, $\epsilon$, may be given by a tensor rather than a scalar.  Now the orientation of the surface is not the only property of the material to define a direction, and the E&M boundary-value problem must be solved again; this time it doesn't lead to Snell's Law, especially if the relative orientation of the optical axis (or axes) of the material and its surface is a wonky angle.
