Any kind of glass/plastic element put in front or behind the camera lens would affect the quality. The only thing is how large is the degradation and whether it is noticable in our daily usage. Many photographers would actually advise you to get at least a multi-coated UV filter. Personally, I would avoid Hoya non-coated ones. And Hoya multi-coated ones are tough to clean but heard that their professional series are better. I would rather get B+W or Nikon ones.
And it's not only about UV rays etc. The filter actually serves to protect the lens front element against accidental touch, knocks, drops etc. Accidental finger prints still can be found on lens using lens hood. But the filter would actually stop any possibility of finger prints on the front element, provided the filter is never removed.