Nope, no "protection" filter for any of my lenses all the time... I simply don't want anything getting in the way of taking a great shot. After all, I bought my lenses to take photos, not to coddle and protect them. Thirty years shooting, 30,000 to 60,000 images a year.... have yet to ever have a lens get damaged just with reasonable care (hood when shooting, capped when stored).
Yes, I have filters for various purposes and I don't hesitate to pull one out and install it when it serves a real purpose. This includes "UV" filters for "protection" if circumstances actually call for it (which happens three to six times a year... maybe). I'll usually use a filter shooting at the seashore, salt spray is nasty stuff and hard to clean off. I'll also use one shooting in blowing sand storms, or sometimes at sporting events when there's risk of flying particles. But the vast majority of the time, I will not use a protection filter. Putting one on a lens 24/7/365 seems utterly counter-intuitive to me.
If using a filter, there will always be some image quality degradation... You are forcing light to cross two additional air-to-glass boundaries and that will always have some effect. It might be very little loss with a top quality, multi-coated filter in most situations... But in difficult lighting even the best will show some increased flare, lower contrast, reduced color saturation, more chromatic aberration than a bare lens will. Always remove all filters when shooting into the sun or other really strong light sources. Cheaper, lower quality, single-coated or uncoated filters can cause issues all the time... softer images, a lot of increase in chromatic aberrations, lots of flare, interference with AF accuracy, etc.
People cite "a filter saved my lens"... but there is no way to prove that the lens wouldn't have fared just as well or better without the filter. On the other hand, I have seen lenses ruined when a filter got broken, when the sharp glass of the filter gouged the front element. So, IMHO, mindlessly installing a filter on there all the time actually increases risk, it doesn't reduce it. As a result, when using a filter it's even more important to cap the lens when it's stored and use a hood while shooting with it.
There is very marginal increase in sealing to some lenses, when a filter is installed. Of course Canon recommends installing one... Canon sells ridiculously overpriced filters and are in business to make a profit! Lenses that see a small increase in sealing (improved water/dust resistance.... none are ever fully waterproof or dustproof) include the 17-40L and 16-35L, for example. But not any of the 70-200s. None of the IF or "internally focused" lenses will see any add'l sealing with a filter. And any lens that's not internally zoomed is more vulnerable at the barrel joints, than anything the filter will help cover.