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.
Why might you still want to write a resignation letter? Many experts believe that writing a formal or even a basic resignation letter when you're leaving your current job helps make you seem more courteous and professional. However, the real reason to write a resignation letter is to create a paper trail documenting that you have given notice (if your employer requires two weeks notice or some other amount of notice) on a certain date, and to formally kick of the process should there be any legal hiccups (quite rare) with incorrectly processing your final paycheck and last day of benefits.