Informal enquiries for faculty position

If you’re going to send such an email, I suggest you make it short and direct it to either someone you know or someone in your research area. (Hence this advice is mainly for research universities.)

You can introduce yourself, say you’re applying, and mention that you’re excited about this job. Taking the extra effort might show that you’re serious, but I honestly find that it rarely helps and can even hurt in the case of a lengthy letter to a busy department chair.

I think if you know someone in the department, that’s when it’s probably most effective; e.g. an email can alert them to your application so they can mention you to the hiring committee, even if they’re not on it this year.

This is an old question but I'll add something because I've had some good advice on this recently, so it might help others who come across this post.

One reason to write an enquiry is that you might get a tip for framing your application. If you state in a few words what you're working on, and ask whether the person thinks you're a good fit, they might tell you (for example) that there aren't any experts in that particular sub-field in the department / committee, so this suggests you should be extra careful that you application is understandable by non-specialists. You might also be able to gauge the relative importance of teaching vs. research, or find out whether an extra item that was not specifically called for (e.g. a teaching dossier), might help or hurt your application. Once I asked about the teaching dossier and they said it would "enhance the application", and once I asked about the research plan/statement, and in this case they then told me that this would be required for the interview phase.

The bonus from all this is that even though you can't count on really helpful tips, you're at least signaling your motivation, and I think this is always a good thing.