I have just arrived to Zurich, Switzerland. I am considering to buy the monthly or annual pass for the ZVV network. However I don't know how many trips per day can I take with one of these. Up to infinity?
As many as you would like (and physically possible) within the zones chosen (some night buses and trains may require additional supplement).
Like your own link says
With a monthly travelcard you can travel as often as you like in the zones you have purchased.