I have 3 cards with outstanding balances. Visa 5k limit, RoomstoGo 4k limit and DiscountTire Card 2100 limit. I have several others but don't carry a balance.
My visa carries a balance because I use for better much everything. gas, groceries, bill, etc, to earn the rewards. balance right now is $1700. I usually make about $1600/mo in payments on this card trying pay everything that use as monthly expenses off immediately. but some other things I've had to use on this card too. I have R2G and DiscountTire card which I used for a major purchases. Furniture for new house and my truck needed new tires a couple months ago. Anyway. the current balance is $960 (0% interest until 6/2016) and $940 (0% interest until 4/2013) respectively. Actually even the Visa has 0% through then end of this year.
I feel like I'm more likely to carry or appear to carry a balance on the Visa than the other two, but I don't want to keep the balance that hight either. So knock out the the Dept cards or the Visa? Afraid if I do the Visa. The balance may just be up again in a couple months anyway whether necessary or not.
TU score 760
I would pay the 04/2013 0% first since the incentive will end first.
Pay the $940 with 0% until 4/2013 first, since you're less likely to run that back up, and it should hopefully remain at zero. Then work on paying the Visa, since that only has 0% interest until the end of this year.
Let the 0% until 2016 sit with just minimum payments until everything else is paid off. I'd even let it sit until closer to the time the 0% runs out, and apply any extra money to other debt that has interest, like a car loan or mortgage, then just pay off that card right before 6/2016.