Is it beneficial for the applicant to mention other universities she is applying to? Going through the application process for several Master's Degrees, I have come across universities that ask what other programmes I am applying to on their application forms. It has been already discussed that there is no obligation on the applicant's part to answer them, but what is the best thing to do from a strategic standpoint?

Do universities frown upon applications to a lot of other places because of the risk that a candidate they admit will accept another offer? Do they gauge the level of confidence/ambition based on how selective other programmes are? How does it affect one's chances? Are there any other considerations?
From a strategic viewpoint it's best not to reveal this information. Revealing this information would not benefit an applicant in any way.

For example, if you tell a second-tier school that you're applying to lots of first-tier schools, it becomes a bigger risk for them to give you an offer. 

I would suggest omitting this information from your application if possible.