I have about 10 LED flashlights. ranging from cheap ones to expensive ones. my question is if i take the batteries OUT of them and just put the flashlights away, will it cause them any damage by not being used?

They should last a very long time if you keep them dry and under 200 degrees. (They don't mind cold, I've seen them work in liquid nitrogen)

Any device with a switch is happier with frequent use. Most contacts will oxidize when deprived of the wiping action of on and off cycles. We all know how flashlights have always required shaking now and then, just to wipe the contacts clean. This does not apply any more or any less to LED flashlights, though.