Yes, it is ideal for all antennas and radio equipment to be attached to a common ground. Your house wiring does this for things with plugs, but you really should ground your antenna. If you have no access to your house's ground or a grounded cold water pipe, you will have to make your own ground. A simple wire leading into the ground won't work. You will need a copper rod, 4-8 feet (depending on the climate / ground moisture) driven into the ground, less than 9 feet from the house if possible. Then connect it to a ground block.
This protects well against static buildup in your antenna. Static is the most common cause of damage to radio systems. An actual lightning strike is much more rare. If you do happen to get a direct primary strike on your antenna, grounding can't help much, and you would be better off worrying about the grounding wire catching fire. Don't worry about direct strikes unless you live on a plain or your antenna is the tallest thing for miles, as lightning is much more likely to hit trees and power poles than an antenna.
Again, the idea of the grounding is to reduce the probability of getting hit in the first place and to continuously bleed off small static charges that can damage your equipment.
