Lens caps are for storing lenses away when not being used. If a lens is on a camera, even if the camera is in the camera bag, I don't have a cap on it. I use UV filters and lens hoods. I've done this with SLRs as well as rangefinders as long as I can remember and it's a great way to prevent taking a picture of the inside of a lens cap.
I keep a cap on to prevent dust. Constantly cleaning dust off of any glass surface can't be good for the glass (especially expensive glass, filters included) - fine scratches will appear before long - good for lowering contrast by diffusion, though.
On some dry days the filter is like a dust magnet.
"Pictures are not incidental frills to a text; they are essences of our distinctive way of knowing." Stephen J. Gould