As far as the polarizing goes, basically nothing.
However, a circular polarizer has a secondary layer, which then unpolarizes the light that has passed through it.
So it cuts the light at '90 degree' as per a linear polarizer, but, as it de-polarizes the light again, it helps with focusing methods which require splitting a light beam and then re-combining it.
If you stack circular polarizers, they will not work as per the standard test for a polarizing item.
If you stack linear polarizers, then they will pass the standard test for a polarizing system (i.e. as you rotate the polarizing field, you will go from X% blockage to full blockage).
I use linears with my 400d and have never had a problem.
However, on automatic focusing systems, it is usually the pro-rata advice that circular polarizers be used.
Edit:
A polarizing filter cannot be reproduced in photoshop. Just as an infra-red filter cannot really be reproduced either.
Next on the list would be ND grads as far as I am concerned. They can be reproduced, but, you risk over/underexposing.
ND filters with high blocking numbers are also important. I had a play with some 30 second exposures, these would not be possible during daylight without NDs
Last, and probably least used, but nice is an IR filter.
After those four, then I reckon any other usual filter can be easily reproduced in photoshop.