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.
After that, you're ready to close out your letter and move on. The basic closings are fine here__again, you don't need to go overly sentimental or formal, but you should also write as if it will be read by anyone at the company. And with that signing flourish, you're done! You've resigned, and you're ready for your exciting new job.