If you are currently drinking more than 5 cans of diet Coke a day, you need to ween yourself off. Quitting caffeine cold turkey can cause blood vessels in the eye to rupture. reduce by a can a day every couple days, buy a water filter (britta makes a water bottle with one built in) and drink that instead. Worked for me.
If you just stop drinking it at all, the headaches go away in a day or two. During those couple of days, take Excedrine. I had the same problem with Dr. Pepper. Get some Mio or Crystal Light water flavorers, it'll help get you to drink water but still satisfy that sweet craving.
You can start a drink journal and switch to water. Get rid of all the soda in your home and get alternatives that can distract you from drinking the diet coke. Since the symptoms will be disturbing and hard to deal with, you can only get the drink once a while and replace the rest of the days by taking water.
If you are drinking a lot of soda why not get the caffeine free and start mixing 1/2 and 1/2 with your regular soda. In a week or so make it 1/4 caffeine and 3/4 regular. after that just the caffeine free or better yet just drink juice or tea or water. Soda, any soda, leaches minerals from your body and can cause problems.
Go through that 3 day hump. It's like smoking, you quit, NO diet coke, for three days, you're alright, you won't crave it anymore. I was once addicted to coke....cane, JK, COKE, quit for three days, and I was A-okay.
If you still want the caffeine and the taste of soda but, your body doesn't like the aspartame you could try a soda they sell at health food stores. It tastes just like diet coke but, sweetened with Stevia. You'd be surprised how good it is. It is more expensive but, your health is worth it. :)
Do research on the dangers of diet coke, and maybe you will scare yourself away from it. Exercise more, and get more oxygen to rid yourself of the headaches. Also try Perrier, it takes getting used to, but its good!
Why do you want to get off of it completely? I think a regular soda has 17 teaspoons of sugar in it but a diet coke??? Try one of the Zero Cokes in the black can. I'm not advocating drinking any soft drinks cause I don't drink them. Are you pregnant? If so you have to get off according to the docs but I didn't and the baby was fine. You might substitute it with iced tea with lemon. Tea has less caffeine. If you have a headache and feel sluggish take some aspirin or something comparable and get some rest.