Yes, it is also a good idea to replace both the strut mount and the strut boot when replacing struts. The strut mount optimizes suspension performance by providing a smooth steering response and reducing vibration. Strut boots will protect your new struts from dirt, dust, salt and leakage.
Video: The KYB Garage: Strut Mounts and Boots in depth.
Video: YouTube: Strut Mounts and Boots in breif (30 second video)