When light gets reflected from a dielectric surface (like the glass of your windshield), the two polarization components of the light don't get reflected by the same amount. The coefficients of reflections for both polarizations are called the Fresnel coefficients.
More details here:
http://en.wikipedia.org/wiki/Fresnel_coefficients
According to these expressions, there is even an incidence angle where one of the polarization components is completely transmitted. This angle is called the Brewster angle.
http://en.wikipedia.org/wiki/Brewster%27s_angle
For example, if the angle of incidence of light on the windshield is at the Brewster angle, only one polarization will be (partly) reflected. This means that this reflected beam has a well defined (theoretical) linear polarization.
If your glasses are oriented to filter this remaining polarization component, you will not see any reflection from the sun through your glasses.
When you tilt your head, you tilt the polarization axis and some light will pass through again. The intensity transmitted is given by the squared sine of the angle between the polarization of the light and the axis of your polarizer.
This is also why photographers sometimes use polarizing filters to take pictures—to enhance or reduce these reflections.
Edit to answer your edited question :
As you can see from the first WP link, there's a fairly large band of incidence angles for which one polarization is reflected much more than the other one. That alone could explain why so many object polarize so well the reflected light you see.
An additional factor I can think of, would be that for an object to reflect light towards your eyes, it has to be at a specific angle. Depending on the position of the sun in the sky and yours relative to the object, it is not surprising that a large amount of objects reflecting light towards you are somehow not too far from the Brewster angle.
Why not finding a flat piece of glass (a watch for instance ?) and experimenting for yourself. Don't burn your eyes with the sun though !
What you are seeing is stress in the window resulting in birefringence: the speed of propagation of polarized light depends on the direction of polarization.
In the setup you have, the light in the sky is partially polarized because that's how Rayleigh scattering works; this partially polarized light is transmitted through the window where it rotates (because of the birefringence) depending on the stress. The polarizer on your camera acts as the analyzer: some of the polarized light will be more at right angles while other light is more parallel to the axis of the second filter.
Now birefringence is a function of wavelength: so different colors will be rotated by different amounts, and will be more or less attenuated. And this is what gives rise to the colors.
Here is an example of an image of a plastic box with in built stresses viewed through crossed polarizers source:
UPDATE - why Rayleigh scattering leads to polarized light:
In this website we read:
The most common example of Rayleigh scattering is the scattering of visible radiation from the Sun by neutral atoms (mostly Nitrogen and Oxygen) in the upper atmosphere. The frequency of visible radiation is much less than the typical emission frequencies of a Nitrogen or Oxygen atom (which lie in the ultra-violet band), so it is certainly the case that $\omega \ll
\omega_0$. When the Sun is low in the sky, radiation from it has to traverse a comparatively long path through the atmosphere before reaching us. Under these circumstances, the scattering of direct solar light by neutral atoms in the atmosphere becomes noticeable
In Rayleigh scattering, the electrons around an atom are a driven simple harmonic oscillator: classically, you can think of it as a negative cloud that can move with respect to a positive center, and if you could displace it, it would vibrate around its equilibrium position with some frequency $\omega_0$. Now when you excite this cloud with a transverse electrical signal (EM wave like light) it will emit light mostly at right angles to the axis of excitation - in fact there's a $\left(\frac{\omega}{\omega_0}\right)^4\sin^2\theta$ term in the intensity distribution. This both tells us that the intensity of the scattered light drops quickly for longer wavelengths (the key is blue) and also that when the sun is to your right, the polarization of the sky will be in the up/down direction (perpendicular to the line from the sun to the point). This is explained in more detail at this website on polarization which is also the source of this animation that shows the direction of polarization that you expect:
Best Answer
Back car windows (and most side windows) are tempered for safety as you noted. The windshield is laminated.
This process is usually done by blowing cool air on the hot glass (after forming for example), this create surface stress in the glass, this energy is released when the glass break, fragmenting it.
What you see here are the marks due to the shape of the cool air nozzles. You will notice different pattern on different models due to the securities of the equipment used. The air nozzles make the cooling slightly inhomogeneous,thus the stress is can have a stronger direction making the glass slightly birefringent. Birefringence is well seen using polarized light and detector Photoelasticity
The light coming from the sky is partially polarized, light from reflection on dielectrics (like glass) also (depending on the angle) which explains your observations