As a newspaper shooter I kept decent quality UV filters on all my lenses, both to protect the front elements from breakage, and so I could be a bit less delicate when I had to clean the front of the lens in a hurry. It's pretty much a myth that it degrades your image noticeably, unless you buy absolute sh!t filters.
Today, I only shoot part-time, have much less expensive gear and don't keep filters on any of my lenses. I keep lens hoods on when shooting, and caps go on when I put them away in the bag. It's just not worth it to me to buy filters for the level of gear I have when I shoot in fairly controlled and clean settings; e.g. mostly indoor portraits.
I think most photographers put way too much emphasis on getting that last .001% better image quality. Modern lenses, even inexpensive kit zooms, are pretty darn sharp and a decent UV filter isn't going to hurt.