Paying phone and utility bills counts towards you score as well. We've bought two cars and a house with near zero (or zero for many years) credit card useage. No problems at all.

Our credit score were upper good before and near perfect now. We've not used a credit card in eight years.

You can get a free copy of your credit report once a year from each major company - you could go ahead and order them just to see where you are at.