Yes! Don't just cut back, cut them off!!! Once you have paid off all of your debts, there will be no need for them anymore. The LAST thing you need in an emergency is MORE DEBT! The idea of keeping a credit card for emergencies is ridiculous.
Create a starter emergency fund of at lest $1000 in a money market account with check writing abilities. Then, write down all your debts smallest balance to largest (forget the interest rates. If ya'll was so awesome with math, you wouldn't have debt, so lets try it this way :} ). Pay the minimums on all the cards except for the smallest balance. To that one, pay the minimum PLUS any and all extra money you can find. Stop drinking Starbucks, sell stuff, cut back on everything. Put all that money to paying off the smallest debt. Then once the smallest is paid off, put the amount you were paying on the first debt towards the next smallest debt PLUS it's minimum payment. Do this rotation until you are out of debt. Attack!!
When all your debts are paid off, put all the money that you were using to pay off your debts in the money market account that holds your starter emergency fund until you have saved 3-6 months of living expenses. This will insure that you will never need credit to cover emergencies, and if you lose you job, you will be able to pay the basic necessities.
After this, you will never need credit cards again. You will pay cash. I have done this for YEARS and have never needed a credit card. If there is something I need, I pay cash. If I don't have the cash, I don't buy it until I have saved the cash. I can bargin with cash to get discounts that can't be done with credit cards.