I'm going through a similar thought process right now. I think the general format that mc listed fits and works well, as long as you can find a way to include some of your personality in it. For me, it comes through in my writing style.
The most helpful thing I've found is to do some research on the theatre you are writing to (even if it's just looking at the website and looking through the names of the important players to see if you've worked with someone before). If I was hiring, I would appriciate the time by a potential hiree if they made an effort to find my name (website or calling) and addressed the letter directly to me.
Name dropping too heavily in terms of my career feels forced and cheap (to me), but anything to get noticed right? Hopefully your resume has that information and can be impressive enough.
Another thing I like to do is have someone else read my letter before I send it out. If you have a roommate, or someone else close, they'll give you the best feedback on the general flow and content of the letter. If something doesn't make sense to them, most often it's not just because they "don't work in theatre," but it's because your sentence structure needs looking at.
Hope that helps.
Jon