This is one of the biggest topics of debate when it comes to photography and lenses. Should you use a UV filter on your dslr? Well some big photographers do not. Some do. Here is my experience and opinions on when you should or should not use them.
Reasons to use UV Filters
First off, UV filters are suppose to cut down UV light, but really modern lenses and sensors now have advanced coatings on them so it's no longer necessary to add extra filters for UV light.
The main reason to use a UV filter is to protect your lens. And this is true in more than one way. First and most obvious, it's nice to have them incase you accidently bump your lens on something breaking your cheap UV filter instead of chipping the front element of your lens. This is even more important when you have expensive lenses.
UV filters are also used to weather seal your lenses. A lot of Canon or Pro lenses are weather sealed, but not completely until a filter is screwed onto the front. So if you're shooting near water falls, in the rain, on a boat or anywhere that might have weather problems, you might want this extra protection.
UV filters aren't just used to protect your lens from physical damage but also can be used to keep them clean. Here is an example. I was shooting the Santa Monica pier one night when the waves were about three to four feet. It was throwing up a salty mist that would collect on my dslr and my lens creating a sticky film. When I tried to wipe this film off it would smear everywhere. Then it gets on your micro fiber cloth and you have to keep using clean cloths to try to get it off, in my case the inside of my shirt. Luckily I had a few filters so I could just swap them out and put on a new one instead of having to clean the existing one. The last thing you want to do during a sunset is waist vital minutes cleaning lenses and filters.
Here is how my photo from that night turned out.

Other lenses like the new Canon 40mm pancake lens also can be difficult to clean. The lens is set into the body making it easy for edges to collect a lot of dirt and dust which are hard to get out. If you have a UV filter on, then you only have to clean a large broad piece of glass.
Reasons not to use UV Filters
There are a few reason photographers stay away from UV filters. They can increase the flaring on your lens. Especially if the filter isn't coated very well. If you get a UV filter make sure you get one that is multi-coated. This helps get rid of the flair and reflection.
There is an interesting article I read on lenses and coatings. You should check it out at CanonRumors All About Lens Coatings if you want to know more. To summarize; glass reflects some light, so the more glass you add on your lens the less light gets to your sensor, like 4%-1.5%. The advanced multi coatings keep light from reflecting allowing more light to pass through the lens resulting in a higher contrast image. So an advanced coating, multicoated both sides will only reflect 0.5% of the light.
On some lenses like my Canon 70-200mm f2.8L USM IS II, adding a UV filter can cause more vignetting. In this case you might have to get a Slim UV filter which are harder to find can can cost more money.
Some say a lens hood can provide all the protection you need from physical damage. And this is true. On many lenses I use the hood is so massive that there is really no reason you'd ever have to worry about something hitting the front element.