Steve Perry of Backcountry Gallery has a multitude of great, down-to-earth photography how-to videos, but the latest one tackles an age-old question we've all had numerous fights over. In spite of Perry's self-proclaimed non-scientific standards, perhaps we can finally put this one to rest.
Perry tests numerous aspects of lens and UV filter strength in the tests done for this video, including some scratch resistance, overall strength, strength of the front element with or without a filter on, strength of the filters themselves, and other effects of bumps and drops on lenses.
The conclusion is more thorough in the video, but in short, aside from protection against some scratches and dust in certain circumstances, filters don't do much at all to protect your front element, or the rest of your lens for that matter. When shooting digitally, they don't even have an effect on your image since digital sensors are not sensitive to the blue UV-created haze that shows up in many landscape film images. In fact, they merely pose a greater risk of introducing ghosting and flare with specular highlights. And if your filter breaks on a fall, no, it almost certainly didn't protect your lens from breaking — your lens would have been just fine, regardless.