The short answer is YES, you can have too much water pressure.
Water pressure that exceeds 80 PSI can cause water damage to your house. Residential faucets, valves, and appliances such as refrigerators, stand alone ice makers, clothes washing machines, dish washers, etc. are rated for water pressure up to 80 PSI. Water pressure in excess of 80 PSI can cause damage to internal parts such as O-rings and tubing connections. Failure can be in the form of only a small drip or complete failure which can flood your house.
If your home has water pressure in excess of 80 PSI, the only way to reduce the pressure is to install a Water Reducing Valve. This device needs to be installed between the water meter and the house. Most pressure reducing valves are installed just before the water pipe enters the house, usually at a hose bibb.
Picture of a Water Pressure Reducing Valve