Whether or not you smile or choose not to smile in your headshot goes back to the first step of the whole process—what are you trying to achieve. Is it a corporate shot or an actor’s shots. If your an actor, does a big smile represent you and what you want to communicate to your audience, namely, agent or casting director? Are you typically looking for commercial work? Are you a more dramatic actor? The simple answer is do what best represents you and the type of work you hope to get. It use to be that people would have a commercial shot done (where you are smiling), and a theatrical shot done (where you are not smiling). I’ve heard people say this has fallen out of vogue but I still think it’s a good idea to do both—which kind of sums up my answer to the whole thing: try and do both. Take some stuff with a more serious look and then take some stuff with a smile. The smile is harder to pull off. It may take your photographer a few takes to pull this one off.
For corporate or any other non actor’s purposes the question is really the same: what are you trying to accomplish? There really is no always yes or no to something like this. You should tell your photographer what you are trying to achieve and let him achieve it. Hopefully this will be me. Thanks for reading!