Uhhh you can't take something off your credit report. ;)
They count, but they're not really what's considered 'building your credit'. It's good to own a credit card and have it open for many years while maintaining relatively low balances. You're trying to have a thick credit file.
Remember that different companies will have different standards for what they consider good credit. The time when this often smacks people in the face is when they go to purchase a car or rent an apartment.