That's pretty it, usually you buy a UV filter to protect the lens. My question is do I need the UV filter even if I'm using a lens hood?
The hood protects the lens of physical impact from knock and obstacles. It also reduces flare and keeps image quality to what the lens is capable of.
A UV filter protects against flying dangers such as sand, salt and other elements. While doing so a UV filter is detrimental to image quality as it adds additional reflections from another glass element in the optical path.
Therefore in most cases you should ONLY use the hood. If you are in proximity of sea-water splashing or flying sand, then you should but a UV filter too. Since flare can still be a problem, it is best to do both if you can.
I have had a filter glass very badly smashed while carrying a camera with a filter plus a lens hood on.
The filter was very badly starred - without it the front lens element was almost certain to have been damaged beyond practical use. The filter had been struck so hard that it distorted enough to make removal very difficult. Despite this the lens was undamaged and gave good service subsequently. I was far from home (Qingdao, China) with a minimum of lenses with me and loss of that lens would have put a severe dent in my excessive photo taking tendencies :-).
Conclusion - the hood alone does not offer full mechanical protection.
Effect of UV filters on image quality:
Doing justice to this subject requires flame shields, thick skin and much time. In lieu of these, below are some links to others efforts. Many of these came via the stack exchange thread sited by @mattdm
This extremely interesting and detailed test UV filters test by LensTip.com describes testing of 20 UV filters using a Hitachi U2900 Spectrophotometer. The test runs to 24 internet pages, mainly due to there being one detail-page per filter, but the surprising and useful results are on page 4.
I will not specify brands below. Each filter detail page also has with and without comparison photos showing the image results and comparison of these comparison pairs for various filters is extremely illuminating. To reduce risk of incineration and siege I'll leave it to readers to look at the article for themselves.
As a guide, the blue light used to drive the phosphor in a typical white LED has a wavelength of about 450 nm.
Optical transmission of their worst rated filter:
Optical transmission of their best rated filter
Here is a graphic demonstration
Below is a photo taken with my smashed filter attached. At that stage I was unable to remove it by hand !. Pieces as subsequently removed with due application of ultraviolence shown as inset. Red lines on photos show some of the visible aberrations.
Snapshot, internal flash, self timer, smashed filter, other excuses ... :-).
Here is a very little of the material available on this subject - much is subjective opinion.
Added - new fatality - May 2012:
I'm not intending to make a habit of this - honest :-).
You can also purchase a NC filter (stands for neutral color) if you don't need UV protection. I have a few of these from nikon. http://www.nikonusa.com/Nikon-Products/Product/Lens-Filters/2479/52mm-Screw-On-NC-Filter.html
As long as it's a multi-coated filter, you shouldn't have to worry about reflections in the optical path.