Although newer iPhones get substantial value (iPhone 4S + 64GB AT&T is up to $150 today), iPhone 3 and 3GS are rapidly becoming worthless in the US. Your phone is may still be worth money in a rebate or gift cart in USA if you exchange it as part of a phone purchase. Apple has an official relationship with PowerOn where the staff in each store checks market conditions from that third party and quotes you an offer when you are shopping.
Apple's plan is documented at http://apple.com/recycling and currently in the US, you can only trade in one device for each iPhone purchase. You can go to that site now and see if they will offer any money, but I'm seeing $0 currently.
Apple staff are trained in evaluating the condition of devices, so you'll get a better read on the price you'll get by having that second opinion. Some people feel their phone is flawless when it isn't. Others mark a phone down for things that would actually fetch price for excellent condition. You can do a little research before going in to the Apple store on:
- http://ebay.com (prices here will likely be both higher and lower than what you will get from a company that does Apple's trade in which means you have to do more work to get a fair number)
- http://amazon.com (search for your model and look for Trade In in the right side of the web page under the buy now/add to cart button)
I would also research what your local cell carriers have for current promotions. If there is an in-store, verifiable special. You can ask Apple Retail to match the brick and mortar offers if there are case / charger deals locally when you buy.
If Apple's deal isn't good enough, look for a carrier or Radio Shack that have $50 for any phone trade in and see what's the best deal overall. I can't imagine it not going for $15 if you put it on ebay for 0.01 and no reserve, but that's a bit more of a gamble than if you were to get an offer from a company that buys used devices.