This late entry delves into an academic niche that was not explored in the recent Cover Letter Contest. It did not make it into yesterday's poll, but the letter makes the important point that some CLs are written by people who already have a faculty position but would like a different one.
In real life, of course, you could just send in your application; there is no need to explain the CL why you are thinking of leaving your current job, unless you want to explain it.
Dear FSP,
Sorry for the late application. I am currently, in my 4th year of tenure-track at University X (have to submit my tenure app at the beginning of my 5th year here), and I was working on journal papers and proposals all through the break that I didn't realize it was Christmas or even 2012 yet. I am interested in applying to your University Y, preferably to obtain a tenured position, but in reality, I'll take anything you have.
To make a long story short, I am DESPERATE.... did you hear me -- DESPERATE to get out of this male-dominated, chauvinist ****hole department at University X. I am decently funded. I have slews of low-quality journal papers because my university emphasizes quantity for tenure, and I can't focus. Please... get me out-of-here. I specially chose your university because it's near me, and we can't move because of my husband's job and our underwater mortgage. I'll work for pennies if you just treat me with some respect.
Yours truly,
burned-out neurotic prof