What happens if you pay only the minimum amount of each month towards your credit card bill?

It depends on your credit card and the type of it, i'd not use it until i pay the whole debt.
My friend received and email saying if he doesnt pay he wont be able to open a bank account the the whole country for 2 or 3 years i cant remember, but that was in turkey. You can ask your bank they would tell you the exact right answer.