Should individuals try to avoid online surveillance by the government?

In a recent comment thread on NoodleFood, there was a debate over the extent to which a person's use of Internet tools such as cloud storage, password managers, wifi, smartphones, etc. exposes him to surveillance by the federal government. It seems to me that any serious effort to avoid using these tools would require forgoing many of the conveniences that make the Internet such a value -- and there is still no guarantee that such avoidance would stop the government from spying on you. Since our government does have many improper powers, but it is nowhere close to being a dictatorship, is there any value in curtailing one's everyday Internet activities to avoid surveillance?