To filter or not to filter, that is the question. I'm really glad Kai has addressed the issue, since I think it's been overlooked by everyone else (apply a massive amount of sarcasm very liberally here... this topic has actually been discussed ad nauseum here and on every other photography forum in existence).
Actually, in my experience it can go either way. I've seen more than a few lenses actually damaged by broken filters, when the sharp shards of glass from the filter were driven into the front lens element, scratching or damaging it or the coatings on it. Would the lens have been better off without the filter? Who knows! Without investing in a few hundred or thousands of lenses and doing a long series of destructive drop tests to find out, there's no practical way to prove anything. But it's equally impossible to prove that a filter has ever actually "saved" a lens.
Yeah, I've got "protection" filters for most of my lenses. They're stored separately in a neat little stack in my camera bag for use in those rare situations (shooting out in a sand storm, for example) where they might actually serve a purpose. I also only use high quality, multi-coated filters that do minimum "damage" to images (usually at least B+W MRC or Hoya HD/HD2 or similar).
I use UV filters instead of "plain/clear protection" because even on digital there occasions that a UV filter can be used to reduce bluish haze, such as occurs in distant shadows of scenic shots. So, at least they serve dual purpose (where-as plain/clear only serve as protection), even if only rarely needed.
Yes, a hood generally gives better protection than some thin glass filter ever could... Plus a hood can further help with contrast and color saturation, by reducing oblique light that's striking the front element of the lens.
When I bought a Canon EF-S 10-22mm lens, I really didn't want to use it with a hood. It's matched hood is really large diameter, sort of a small Frisbee, and inconvenient to store and carry around. Besides, I knew from reviews that the 10-22mm is one of the most flare resistant lenses in the ultrawide category. So, even though I tend to use the hoods on my other lenses pretty religiously, on this one I thought maybe I could get by without the matching hood, and decided to do some test shots....
Left: 10-22mm, no lens hood. Right: 10-22mm with matching EW-83E lens hood. (Note: The clouds moved slightly while the hood was being installed.)
Okay, okay! I'll keep the hood and use it!
Finally, if you don't already have one, get a good Circular Polarizing filter. That will improve images contrast and color saturation in a lot of situations, too. What a C-Pol does is mostly only allow "aligned" or non-oblique light to pass through, blocking oblique light striking the filter. This reduces reflections, which are essentially scattered, stray, oblique light. And when reflections are reduced, in a lot of situations you will see significant improvement in both contrast and color saturation. You won't want to leave a CPL filter on a lens all the time, though... since it will also "cost" one to two stops of light, causing you to need higher ISO and/or longer exposures.
A C-Pol is rotated to increase or decrease it's effect. This makes them a little inconvenient to use inside a lens hood (but one is still recommended... just remove the hood temporarily to adjust the filter).
Quality and multi-coating of a CPL is even more important than most other filters, because a C-Pol is actually two layers of glass (and four surfaces requiring coatings). They also are more expensive. But, as one of the few filters that cannot be replicated in digital imaging post-processing software, Circular Polarizers are one of the most important and useful.
Note: There are also Linear Polarizers. However, those will interfere with modern cameras' autofocus and, in some cases, metering systems. So a Circular Polarizer (aka C-Pol or CPL) is what's needed.