I have never liked the idea of putting UV / Skylight filters on my lenses. I did, a long time ago, but with experience, I found that they can often times "hold back" your lens' full potential. Although, there is that argument that these filters help minimize haze and, at the same time, help protect the front element of your lens. I'm sure you have all experienced when you buy a new lens, the salesman will typically advice and convince you to buy these filters for the reasons mentioned above. That's okay, it's their job to sell stuff. No offense meant to salesmen out there. Usually they'd say it "costs almost nothing" and the uninitiated will usually be convinced . . . and believe this religiously that they can never ever again buy a lens without "protection". This is debatable, of course, but my personal opinion is . . . don't bother with them.
Cuts haze? I don't believe so. Modern lenses have coatings and elements that already does this, if not something similar. Lens manufacturers make their lenses to the best they can without the need for third party additions to improve their performance. In fact I have had filters that actually degrade image quality produced from my lenses. I tested them with camera mounted on a tripod and in manual settings, then shot with and without filter. I found that without UV filter, the resulting photos are clearer and sharper. Cheap UV filters (and even CPL) tend affect the lens' sharpness.
Protection for the front element? I don't believe so either. That job belongs to your lens cap (and partly the lens hood). I've even seen photos showing broken skylight filters to demonstrate how it will "give its life" to save your lens. But I think that's BS. Those filters are much thinner glasses than any of your lens' glass elements. Yes, even the cheapest of lenses. Naturally that filter will be the first to break . . . and rather easily . . . during an impact. I'd be more worried of the shards and grits scratching the front element of my lens. Mind you, on the opposite, I've also seen demonstration videos showing how tough those lenses are. They definitely don't need protection from a thin glass. Watch this durability test by DigitalRev TV from 3 years ago and fast-forward to 9:00. Watch at your discretion, some scenes are extremely violent.
So to sum up what I've been trying to say so far - Don't put cheap glass in front of your expensive glass.
My Fujifilm X100S is a different case. I have a UV filter permanently attached in front of its Fujinon 23mm f/2 lens. But let me explain. The X100S has a fixed lens and is my every-time-carry-around camera, always ready for action. I want the ability to just pull it up to my eye and shoot.
In other words I'm using the UV filter to act as an "invisible lens cap" together with an aluminum lens hood. That is my protection for the lens's front element. Let me add, this is not some cheap filter. It's a B+W brand UV filter with anti-reflective coating. To my knowledge, B+W is the world's best manufacturer of filters . . . and arguably the most expensive. But it's okay with me. That fixed lens on the X100S is high grade and DESERVES expensive glass in front of it. Because of the anti-reflective coating, it kind of has no effect on the performance of the fixed lens. It's like I paid for an expensive glass that is "invisible". Perfect.
The only other filter I have is a 3-stop B+W ND filter for my Fujinon XF 60mm f/2.4 Macro. And yes, it costs more than its competitors. I'm using it mainly for strobing outdoors. Most of the time I shoot with that lens bare.
I also have 2 rectangular ND grads which I use for the occasional landscape works. I have polarizers but I find Photoshop better (and more convenient to use) at improving picture contrast so I don't bother with them anymore.
So there you go. If you're buying the very best lens your money can afford, for the love of God, don't put cheap filters in front of it.