I install a clear filter, sometimes a UV filter on some of my lenses. Mostly for protection. If I'm using a filter, I always use a top quality filter, mostly B&H. No point using a poor filter over an excellent lens, is there. But some I don't some lenses I can't install a filter...so I don't worry about it. I've experimented a bit...filter-less and with filter with some of my lenses. I can't tell the difference, but then I use quality filter, when I do use them.
I recently installed a B&H filter onto the GH-3 Adapter for my Ricoh GR ll. Reason is some experience dust getting on the sensor. I haven't yet...touch wood...but I thought I would attempt to lessen the likelihood of this happening by installing the adapter and filter over the lens. We will see.
I tested before and after and as before, can't see the difference. With the Ricoh GR ll, I'm using a B+W filter. I also use an old screw mount 49mm metal Ashai Pentax lens cap to cover the adapter/filter. It's a little worse for wear, but adds 'character' to the new camera.
I did drop my K10D a few feet with a B+W filter on the lens. The camera fell hitting the edge of the lens. Thankfully both camera and lens were ok, but the B+W filter absorbed the hit and although the glass was ok, the metal part of the filter had a bit of a scrunch. I was a lucky guy.