When people go 'cash only', one of the first things they consider is if they should literally switch to using cash (greenbacks) only. Or can they still use plastic, as long as the money is coming from their bank account via a debit card transaction?
The argument for the papery green kind of cash: when you run out of money you will have to stop spending, when you spend actual cash you can literally feel your money leaving your pocket, you won't risk overdrafts because you don't involve the banks at all, you surprise people who hardly ever see cash transactions any more, you are more aware of how much money you have when you can actually see it in your hands, and you will never be stuck without funds on those rare occasions when you go somewhere that only accepts cash.
The argument for debit cards: you still retain the consumer protection that a debit card with a Visa or MasterCard logo on it provides, it is safer than carrying around a wad of cash, you are still technically using cash because you are debiting money from your account, and you can still "swipe" your purchases just like "normal" people do.
Unless you have a serious issue with overspending if you use a debit card (ie: you overdraft your account because you can't stop spending with your debit card), I would suggest a combination of the two. For a real eye-opener, you may want to use the first month of two when you switch to the cash-only lifestyle as a cash-only living experiment. Simply cash your paycheck and divvy up the money into each of your budget categories. Pay your bills in person with cash or buy money orders for bills that can only be mailed, then use the rest of your cash for all of your spending throughout the month. This is generally a real shocker, I know it was for me. With a debit card, when you aren't looking at the cash you have, you have a sense of having money that will come from 'somewhere'. So you spend accordingly. This means you spend every last dime because you just know that more money will somehow magically appear in your account any day. When you are using only greenbacks, there is no magically appearing money and when you have $50 in your gas envelope with two weeks left of the month, you do two things--you either drive less to conserve gas or you come up with a way to make some more money to add to the envelope. This is how real economics works--you can only spend the money you have so you either need to spend less or earn more. No magically appearing money, no "maybe I can spend more than I have in my account and somehow get money into the account before it overdrafts".
So after cutting up all of my credit cards, paying off and closing all of my credit card accounts, and the eye-opening experience of spending only cash for a couple of month, I settled back into using a combination of cash and debit card. Now I'm not afraid to use debit cards like I used to be since I am always aware of the balance of my accounts. I have three separate bank accounts which all have debit cards. One is for my emergency fund, one is for savings (such as what we use for traveling), and one is for regular expenses. I still like using cash for most of our spending, and I use checks to pay bills by mail. I use debit cards for larger purchases (mostly for the consumer protection), and to purchase things online (like airline tickets or the rare Amazon purchase). I think a combination of cash and debit cards works best but have known many people who seem to do really great using ONLY cash. Which ever route you choose, the bottom line is that using either cash and/or debit cards will save you money AND keep you out of credit card hell.