Some of the Brodit phone mounts do allow for cases, some are even made for the more popular phone/case combination.
You buy a car specific mount that clips onto part of your dash and doesnt cause any damage. This has a mounting surface to which you can then attach the device specific mount. These are either passive mounts (just hold the phone) or active mounts (they have a charger and built in usb/charger plug that the phone slides into). Some of the latter use cig plugs to charge, others are for wiring into the fuse board and others have a normal usb.