Hi,
The main function of ultraviolet (UV) filter is of course filtering ultraviolet light. This helps reducing the haziness caused by UV light. The result is a more clearer photo. So far in theory.
Nowadays however imaging chip in modern DSLRs and coatings in newer lenses are already able to filter UV so effectively, so that the filtering effect of a UV filter is no longer as necessary/important as it once was.
As a good UV filter has (almost) no impact to visible light, it is very useful as a protection filter for (expensive) lenses. Some lenses are only environmental sealed in combination with a protection (UV) filter, e.g. some L-lenses of Canon. By using a UV filter, the lense's front element is protected from scatches, smudges and maybe also from dusts and splash water. All of my more expensive lenses have a UV filter applied on.
If you are offered UV filters, please make sure that these are multi-coated. Brandwise Hoya, BW, Singh-Ray, Rodenstock are among the best. Lower quality ones might decrease the image quality though.
Polarizing filter is another story. It is the only filter that no photo editing software can emulate. If you are a landscape photographer it is a must have IMO and thus belongs into your bag. Most good polarizing filter are quite expensive. Personally I like BW's pol filter the most. As there are enough good articles about polarization filter, I would rather save up my 2 cents

For example:
http://en.wikipedia.org/wiki/Filter_...phy)#Polarizer
http://www.great-landscape-photograp...ng-filter.html
Hope this helps
Hoang-Tran