If you are inquiring about a tow vehicle and trailer, the answer is no, the tow vehicle collision & comp insurance does not cover damage to the trailer. However, the tow vehicle liability coverage does cover the trailer as long as it is under tow (including damage caused if the trailer breaks away from the tow vehicle while under way). Collision & comp for a trailer is generally quite inexpensive, though, when added as a rider to the tow vehicle policy.
As for liability coverage while the trailer is parked, if you own a home and have homeowners insurance (or the equivalent apartment dwellers insurance) you probably have adequate coverage for your personal liability if there should be an accident to a visitor on your campsite or in your trailer. If you don't have such insurance, you may want vacation liability coverage, which is available from companies specializing in RV insurance.
If you are a fulltime RVers and do not own a permanent residence somewhere, you probably should have "fulltimer coverage", which takes the place of the typical homeowner insurance provisions for liability, personal property, etc.