Should parents monitor their children's online activity

This video made some interesting points about online safety. It mentioned that parents are the first line of defense. They should make sure that they do "walk-bys" and establish rules. They also mentioned that it's actually a good idea to install spyware and monitor kid's activities online.

They mentioned that if you tell them that you will be monitoring it is no longer spying. As soon as you mention that you will be doing it, it's enough to deter a lot of teens and kids from doing that risky behavior.

Do you think this is going too far? Should it be a last resort and only happen if you have a reason not to trust them? Is it something that works or will kids still be able to hide their activity?