Just to add to the discussion.. if you are connecting wirelessly through your company's lan, then they are likely to have a record of where you go and what you do on their router. If you do not hook up through their network, then no, they can't tell where you have been or what you are doing..
HOWEVER, as already been stated, in the event that you were issued your laptop by the company, there may be monitoring software on there. Now for the next big HOWEVER, even though they may monitor what you are doing, unless you signed an "AUP" (acceptable use policy) that stated that you may be monitored, blah, blah, blah, and clearly outlines the expected use of the laptop, they can't monitor you. Or rather, they can if they want, but they can't fire you because of your actions. If they do, they face a lawsuit for invasion of privacy. Even on company property, there are situations where employees have an expectation of privacy. For instance, your boss can not sit and listen to your phone calls, nor can they video tape you in the bathroom.
If it is your own computer, they can monitor your traffic through their server, router, switch, or whatever. That is their prerogative and necessary to protect their network.
Confuse you more?

EDIT: Don't you love how we can make a mountain out of a molehill?