So what activities that I've run have had the highest impact to effort ratio?

Probably "20 questions" and "Telephone Pictionary".

These two take almost zero time to setup, and result in grand times, with people laughing, discussing, and smiling.

A game where the players create the content on the fly is not for EVERY group, but the are so strong for so little prep time that they are probably worth trying.  

They aren't effortless though.
For 20 questions, I created an idea list, so that people that didn't know what to do could look at the list.  typically, they'd then figure out what we were looking for and pick their own thing.
For telephone pictionary, you need merely to go to a store and buy notepads, enough for one per person and also bring some pencils.