Photographic filters: http://en.wikipedia.org/wiki/Photographic_filter
Some people use UV filters as lens protectors. Highly debated, 'kiasu' people get one for each lens. Since it's a piece of extra glass in front of the lens it can also have negative side effects on image under certain conditions. Search for 'lens flare' and 'ghosting'.
Understand first the purpose, then the decision becomes easier.
Yes, you can still put a lens cap on any normal filter. But there are slim versions of some filters. There you can't put on your normal lens cap. But those filters come with a special lens cap then.