I keep on forgetting how to do this so here it is documented for my convenience.
Start Performance Monitor (PerfMon)
Click + to add new monitor.
Enter computer's name
To view connections for a web service
From Performance object drop down select "Web Service"
From Select counters from list drop down select "Current Connections"
From Select instances from list select "_Total"
To view connections for a web app
From Performance object drop down select "ASP.NET Apps v2.0.50727"