Sure, it may sit in the depths of HR until the end of time, but you can be sure of two things: One, your former boss (and future reference) will read it and be impressed. And two, if you ever decide to come back to your company (hey, it happens), it's a very good thing that last thing on file is a great, professionally written resignation letter.
A resignation letter can also help your boss and your company start the transition process, get a replacement for you approved, and start planning internally, etc. The paper trail is beneficial all around. So what should go into your letter? Let's look at some examples of what to do (and perhaps more importantly, what not to do).