I usually pay off my credit card each month and therefore carry a very low, or zero balance. I'm tired of being charged a $29 fee if I choose not to pay a $10 balance in a given month. Does anyone know of a card that only charges a percentage of the outstanding balance for a late or skipped payment fee?

Jim, I think the better question is how can you avoid late payments. Even if you find a card that charges a % of your outstanding balance instead of a steep fixed charge, by paying late you are doing damage to your credit history that will be reflected for 7 years. This leads to higher interest rates when you want to make big purchases such as a home etc.. That can end up costing you thousands of dollars in interest payments. Try online banking where your bills are paid automatically.