Whether you decide to use a filter or not, if protection is your goal, you'd be a fool to not use a lens hood.
A hood actually improves image quality, while even the best filters degrade image quality (though, granted, imperceptibly so with the high quality ones). Except for those few lenses where a filter is required to complete environmental sealing, a filter only protects against the types of hazards that come in situations where you yourself should be wearing eye protection -- such as gravel kicked up at a rodeo. A hood, on the other hand, protects against all the common real-world types of hazards photographers face, including impact and fingerprints. More to the point, an impact that would damage a front element will damage the filter in a way that will often transmit the damage on to the lens, such as by jamming the filter threads or scratching the front element with the broken filter. The hood will actually protect the lens against those types of damage. And quality filters generally cost about as much as repairing a lens with a damaged front element.
For most photographers in most situations, the hood provides all the protection one needs. For many (not most) photographers in many (not most) situations, a filter will degrade image quality. For only a few photographers in only a few situations will a filter provide protection not offered by a lens hood.
The key is understanding the actual type of photography you do and, from that, knowing if adding a filter to your hood (which you should always use) will offer physical protection worth the degradation of image quality. Or, if you regularly shoot in environments in which a filter is actually prudent, you should be able to recognize situations where the filter is going to significantly degrade image quality and be able to make the decision to remove the filter for that shot.
(Of course, this all applies only to clear / UV / protection filters. Polarizers, neutral density filters, and other filters for effects are irrelevant to the discussion. And, of course, there are all sorts of other odd exceptions, such as lenses like the 50 compact macro which is its own hood, the fisheye lenses and their bulbous front elements, photojournalists who should be getting combat pay, and the like.)