Here are all of those iPhone trade-in programs:
The first deal on the list is from AT&T, and here is their link:
https://tradein-program.att.com/home.php5?c=en-us
The offer from AT&T will allow you to sell your used iPhone, and you get a promotion card in exchange. This card is valid toward the purchase of any of the carrier's products and services. The list shown includes the trade-in values for an AT&T-branded iPhone, although other carrier models are also accepted at a lower price. Be sure to click the link for more details.
The next deal on our list is from Verizon. Here is their link:
https://www.trade-in.vzw.com/home.php5?c=en-us
Keep in mind that trade-in value is determined by the condition of your phone and the credit you receive is good toward purchasing Verizon products and services. Either branded or non-carrier-branded iPhones are accepted, and Verizon doesn't assign a difference between their values. Big Red will accept iPhones that have cracked screens and won't turn on, but it won't give you anything if your iPhone has any water damage.
The next deal on our list is from Sprint. Here's the Sprint link for their trade-in page:
https://secure.sprintbuyback.com/cns/
While Sprint's numbers look poor in comparison to the others, keep in mind that Sprint has a new program in which they will meet or beat any competitor's trade-in offer. This means you could make out like a bandit if you are a Sprint customer.
Next up is T-Mobile. Here's the link to their offer:
http://www.t-mobile.com/DeviceRecovery/cell-phone-trade-in.aspx
With T-Mo we see that they are accepting models from all carriers. We also see that values are considerably lower for damaged iPhones. Interestingly, T-Mobile is also offering a price matching guarantee just like Sprint for any trade-in offers, but they will even trump their competitors by $50 bucks starting on September 17th. If you can wait, that could provide you extra value.
The next retailer on our list isn't a carrier, it's Apple themselves. We would be remiss if we didn't include a link to their trade-in program so here it is:
http://store.apple.com/us/browse/reuse_and_recycle
Apple's program is pretty aggressively priced, but you need to keep in mind that they are much pickier about the quality of the device than the previously mentioned carriers. If your old phone is in good shape you could get up to $310 in Apple store credit.
The final trade-in deal on our list is from Amazon. Here's their link:
http://www.amazon.com/Trade-In/b?node=2242532011
It looks like Amazon is very picky about their trade-ins too. On top of that, they have more pricing variations when it comes to carrier branding and even color! As you can see, they neatly create categories to determine the relative value of your device, although it's obviously up to them once they get yours which category it will fall into.
This list isn't meant to be exhaustive, but we intend it helps you make an informed decision. Good luck!