Yes, but make sure that you get the right item. First and foremost, buy the best quality available.
Second, don't make the error that many unschooled camera store sales clerks perpetuate, that UV (or UV/Haze) is just a clear chunk of glass. It's not, it's a color correction filter and you need to pick the right one.
Personally, I prefer a Skylight 1A, and here's why.
Next time you're in a camera store, ask the salesclerk to pull out one of each, then place both filters on a white piece of paper. You will see that the UV has a slightly yellowish cast whereas the Skylight has a slightly pinkish or magenta cast.
The UV's yellowish cast is designed to combat the bluish tinge you get when you shoot on an overcast day. On a hazy day UV light is scattered throughout the sky and makes things look slightly blah-blue. This is why doctors say that you'll get a worse sunburn on slightly overcast days than you will in bright sunlight. It's because the UV light is highly scattered and clouds up the sky with blueness.
The Skylight is designed to overcome a different kind of blue. It's pink cast corrects the blueness in skin tones when people are photographed in open shade. It's a skin tone warming filter.
In these digital days we don't worry about it so much since we're all doing our own color correction in the computer. But back in the day when we had to make transparencies for publication this was a big deal. because color correction cost us money.
So, it's cheap protection, and I can attest to the hundreds of damaged lenses I've seen to make me think it's worthwhile. Even if you're diligently protecting the glass, a dropped lens often dings the accessory ring making it impossible to screw in any other filter or accessory. The metal that particular part of the lens is made from is not particularly malleable, and about a fourth of the times the tech tries to unbend that threaded lip of the lens it will break off.
That's when you'll sure wish you had taken the time to put a filter on your expensive lens.