Well, for starters, if you really buy into the Ramsey plan, you are paying for everything with money you already have. There is no more credit card to save you. Having an emergency fund gives you a cushion when you suddenly need money you haven't budgeted. Such as locking the keys in the car and needing a locksmith to jimmy the door open. *ahem*
Once you have a Baby Emergency Fund of $1000 set up, leave it at that amount until all debts are paid off. Yes, this will mean replenishing it if you have to tap into it. That's OK. That's what it's for! After you are debt-free (except for the house), Ramsey suggests saving enough to cover 3-6 months of expenses. Note he doesn't say salary. We can safely assume that if times were tough, we wouldn't go to the opera or out for a sushi dinner. Just enough to cover expenses.
The nice thing about an emergency fund, in my limited experience, is that it eliminates the need to reach for a credit card when times are tough. After all, we were supposed to have cut them up (we have them in the desk drawer until they are paid off. Paul can't quite cut them up yet. He'll get there.) In my little snafu the other night, it was easy to transfer the $40 from my ING Emergency Fund savings account into the Main Checking account. Now I need to add $40 back in - no biggie. After my next paycheck I'll put it in and we'll be back in business, ready for a larger emergency (which hopefully we won't experience!)
Having an Emergency Fund is what makes the cash system work for me, emotionally. I don't think I could successfully plan for every little bump in the road. This way, it's been pre-planned, in a way. It is a really great feeling to only spend money that we have. I wish, oh I wish, we had lived this way ten years ago! Oh well. Better late than never!