Are you doing work for the company on that machine? If so, they might, depending on what you were doing- that's a talk to a lawyer question, not a free advice question. But if you use their computer and/or thier connection, then yes, they have every right to monitor that. The same way they have every right to require you to maintain a mileage log and justify every mile if you use a company vehicle, or to inspect every purchase made with a company credit card.

Personally, my machines don't do work stuff, I don't even check work email at home. Heck, they pay for my beeper, but only they have the number.

Picard, do you have a reason to be asking a guilty conscious-type question?