There is nothing un-Islamic in using credit cards as long as one does not delay paying the bills. The bills must be paid in total on time. It is indeed haram (prohibited) to pay interest.

Dr. Monzer Kahf, a prominent economist and counselor states: “Using credit cards issued with a condition of interest is permitted only in one way, that is, if you can pay, and you actually pay, within the grace period without incurring the clause concerning payment of interest. This means that you may not transfer any balance from one billing period to another.
Although we all use cards in North America, I only see extremely rare situations where a Muslim may be faced with the necessity to buy a given car or a car at a price that she/he can not afford to either pay cash for it or to take it on lease. This means that under normal situations it is not permissible to buy a car in the USA on interest (especially at this time where all car dealers offer zero interest and many of them with rebate too).”