Working for free has a huge stigma attached to it, and for good reason. If you don't know how to work for free properly, you can be taken advantage of and devalue other photographers' work in the process. That's why there are, in my opinion, only 3 reasons to work for free.
Here's a short comedy sketch that creatively sums up what photographers and other creatives often experience: being asked to do free work in exchange for "exposure."
Requests for free spec work is a big problem for photographers, who lose out when clients demand free photos in exchange for "vague to nonexistent compensation." To show how ridiculous the idea of spec work is, Toronto agency Zulu Alpha Kilo had a guy approach people in other businesses with requests for free spec work to sample their products and services before actually committing to paying. A barista, chef, personal trainer, and architect all responded with indignation; watch their reactions in the 2.5-minute video above.
"Spec" is short for "speculative," and "spec work" is defined by the AIGA (which counts many photographers as members) as, "work done prior to engagement with a client in anticipation of being paid."
This is the classical definition, and it began in the creative industries, where a photographer would shoot images for a desired client and then show them the work in the hopes of being hired. Notice the very important distinction: the work was done BEFORE contact with the potential client. This "free" spec work was not solicited or negotiated.