I think this is the most-asked question in all Internet photodom...and one of the most contentious.
Personally, I do not use protective filters except in certain situations:
1. if I am borrowing a lens from somebody who gave me the lens with a protective filter in place
2. if there is a lot of sand/dust flying, and I happen to have a properly-sized protective filter on me at the time
3. If a lens does not have a cap, I will put a beat-up protective filter on it before packing up the lens in place of a lens cap.
I do get the proper lens hood for whatever lens I am using whenever possible. Nearly all possible contact with the front glass is eliminated this way, though protruding lens hoods do increase the size of the camera, and likelihood of collision with things. The front retaining ring on my Canon EF 50mm 1.2L broke when I hit the lens hood against something. It would not have happened in that particular case if the lens hood had not been attached (and definitely would not have happened if Canon made the darned part out of metal instead of plastic, like they do on most of their L lenses).
I don't like to use filters simply for protection because:
1. Maintenance is a pain. They are magnets for dust, wipe marks, fingerprints, etc.
2. They are more likely to pick up glare than a front element, because they are way out front and totally flat. Combine this with the dust, fingerprints, etc., and their effect on the picture is increased.
3. They are suspended a distance from the front element, thus any items such as the above have more of an effect on the pictures than if the marks/glare were on the front element itself. The narrower the D of F, the less of an issue this is.
4. Unless they are actually plain protective filters, they are designed to have specific effects. UV and 1A filters are designed to affect the image, not just to protect your lens.
5. They are several more unnecessary things to buy.
6. One of them has never saved me any damage to any front element. In fact, the only time a front element of mine got damaged was from the broken glass from a shattered filter.
Other than the Canon incident I mentioned, things have been quite good with lens hoods and a brush off of the front element with a soft brush a few times a day (or less, depending on circumstances).