We actually wait until the rest of the soup is entirely finished and then throw in the noodles. No matter what cooking times the recipe gives, we've found that this is the only sure way to avoid overcooking the pasta. Since most soups are slow-simmered anyway, the extra few minutes won't do any harm to the final dish.
We also cut off the heat when the pasta is still slightly crunchy. The residual heat of the soup will finish cooking the pasta.
Alternatively, you can cook the pasta separately and add a portion to each individual serving. We find this is the best method if we're cooking a big batch of soup since the noodles in the leftovers will continue absorbing liquid - and become mushy - even after the soup has cooled.
What's your favorite pasta soup?
Related: Look! Pipette-Shaped Pasta!