I mostly do it when I'm examining modules in a codebase I'm unfamiliar with.
Theoretically I really like the idea of reviewing code on paper.
But typically, if I'm trying to familiarize myself with a codebase, we're talking dozens of files. Usually I'm going through three, four, five levels of code to see how a request is served up, and then my search will fan out sideways into even more files as I attempt to see what other processes in the application might affect the data I'm concerned with.
To paper? Never. To PDF? I've printed to pdf to get nice looking formatted code for presentations.
I see print as more a brute force bazooka feature to get nice vector graphics out of apps.
* c/p in a gist
* when looking at the gist, print the page in your browser
* save to PDF