i have never broken an element or even scratched one. scratches in the element will not be noticeable until around F/22 or so anyway, and they can be replaced.
in the unlikely event i do drop a lens (touch wood). and, in the event i do, if the very hard yet slightly flexible hood breaks (touch wood again), hopefully enough energy has disapated. otherwise, i'd rather break the element than put optically poor filter glass in front of all of my images. as it is, i hate using circular polarisers and neutral density filters, and only use them when necessary. uv filters were great when we used films like ektachrome and velvia, as they are prone to UV hazing in daylight. fortunately sensors aren't overly sensitive to that area of the light spectrum.
with any filter, i highly recommend multi-coated filters. this will reduce reflections and flare which occur between the outside element and the filter. also, i highly recommend taking the filter off at night when taking pictures of scenes with strong light sources (signs, etc.) as light will reflect off of the flat sensor and the flat filter back down to the sensor, giving you artifacts.
it's like buying a nice BMW, then putting on stickers all over the car which says please don't touch or park too close. it may protect from scratches but it ruins the experience.
if you feel better with a filter for protection, by all means - i highly recommend it - then get a decent one like B+W or Hoya pro1 (avoid the green boxed ones).