Reading up on UV light at wikipedia, it looks like "it depends."
Normal window glass will let in 90% of light above 350nm and reflect 90% of light below 300nm. UVA, which is implicated in long term, deeper skin tissue damage, passes through relatively easily. UVB, which is the culprit of sunburns, has a wavelength of 320nm and below.
Pure glass (SiO2) is almost perfectly opaque to both types of UV light, I believe. Some synthetic, specialty "fused quartz" (SiO2, still) are completely transparent to UV light. UV transparency is also dependent on thickness.
Overall, you shouldn't get a sunburn in your car unless you are really sensitive to UV light and/or are exposed to it for a long period of time. Nice to learn that it isn't perfectly protective, though. Richard Feynman didn't go blind or get cataracts...maybe he was lucky (or was looking through pure glass).
- LostCause