There are many benefits of UV filters, but I would just like to point out that while UV filters will cut down a very very large percentage of problems like algae, parasites, etc. It cannot remove 100%. This is because the UV filter only affects a small percentage of the tank at a time, not the entire tank.
What will happen is that the population of algae, parasites, etc. will change until the rate of growth (reproduction) will be equal to the rate of death by the UV. Now, the remaining populaiton of algae, parasites, etc. may be extremely small, so that the fish may not be appear to be afflicted with parasites at all, but there will be a very small core population ready to spring up if the fish become stressed out.
That said, a lot of people have had success using them. For example, if you use a UV to kill off 99.9% of the ich in the water, then use medications to kill the last bit (medication affect the entire tank so you can eliminate 100% that way) many have found that the length of medication can be much shorter and hence easier on their fish.