Yes. Privacy Is A Constitutional Right Everyone Should Have. The Government And Private Corporations Should Respect Our Privacy. Although, An Argument Could Be Said That This Would Prevent Crime And Terrorism, However Other Measures And Safety Precautions Could Be Used Instead Of Interfering With Regular American Citizens' Privacy And Rights.
Not just online but in real life as well. It is a privilege that should vary with responsibility.
From the time you are born till you find a place of your own, you live under someone else's roof. They pay for the home so it is their call on how much privacy to give others. If your a responsible child, odds are your parent(s) or guardian(s) will give you a fair amount of privacy but if your not, parents may limit the amount of privacy you have. For example: A friend of mine had a kid who would always try to get away with stuff behind closed doors. I helped them take his bedroom door off till he earned it back.
No matter what age, there are some things that should be closely watched or prohibited entirely. These are things either can be used for illegal purposes such guns or thing that are already illegal such as illegal drugs.
Even when you get a place of your own, privacy may be denied. For instance you may have a landlord who has the right to inspect the property, or you could be an ex-con that must allow police to search them or their property at any time. The reason why you get more privacy in a home you own is because you earned the right and the reason why your denied privacy as an ex-con is because you have shown your not worthy of it.
The same arguments can be made for on-line privacy. If you have your own internet connection and computer or other hardware, you have earned the right for privacy but if you are using someone else's connection or hardware, they should have the right to place restrictions and the ability to check and see if you have been honoring them.