In my old High-school, the teacher was able to take control of the screen, see what was on it- even put what was on one persons screen onto everybody elses. Why, this one time he took control of somebody who was using E-mail W/o permission, and changed the last line of his note to his girlfriend from "see you soon Lisa" to "See you soon, Debbie". I can only imagine the trouble he had explaining that.
But, anecdotes aside, some companies have monitoring/auditing of a similar sort in place- the actual screen content could be being viewed for example by a security auditor.
However since for the most part companies trust their employees to use their time for something productive, they probably don't actually go so far as to literally record the actions of employees on such an extended level. They may, however, be able to see that you have been accessing your home E-mail (via network logs), so if this is frowned upon you may still catch some flak.
