I frequently bring up "Task Manager" (hit "control-alt-delete", once only) and open the "networking" tab.
Then I can see an indication of "how much is coming in and how much is going out"
If I am downloading, I expect to see a fairly constant stream of traffic, at 50% or more of the bandwidth capability (say, at 30kb+ on a good dial-up) as long as the site I am downloading from is well connected.
When Windoze Update is running (mine runs automatically) I can see this activity, so I know to expect my aplications to access the web a bit slower.
But if neither of the above scenarios are present, and I still see a lot of internet activity, I would suspect that my computer is running a "Trojan", and possibly being used to attack a web site, under someone else's control. (Which would also seriously degrade my own applications access to the internet)