It also starts the clock for your boss and your company, kicking off the transition plan of training, hiring, and otherwise covering your impending departure. The bad examples here are all too vague. With the last one, you're aligning yourself with company policy, which is good, but it still doesn't tell the reader how much notice that actually is. Be as specific as possible on the time you have between now and your last day.
And sure, this could be an email (all of the same principles would apply), but a letter makes things official in every sense. It also gives you a prop to take along to the face_to_face meeting with your boss, when you let him or her know that you're leaving.