There are a number of websites, plus cell phone and electronic stores, that will buy your old smart phones for cash or offer you a gift card for a trade-in. It has to be in good condition and working order.
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eBay is one of the top sites for selling any cell phone.
The iPhone 3G is averaging approximately $107 to $200 on ebay.
The Motorola RAZR will get you about $20.
Even bag cell phones are being sold on the web. Some are going for $14 to $269 on eBay. The average is about $23.
If you have a more recent model, like an iPhone 5 or 6, some stores like Best Buy will give you a $250 gift card towards the purchase of a new phone.
Older model smartphones will run a bit slower on most data networks, but for basic functions like calls, email and pictures, an older model phone works just fine.
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Before you put up your old smartphone for sale, if you are the original owner of the phone, get it unlocked first. This way it can be compatible with other cell phone services.
Here are some helpful links for selling or trading in your old cell phone:
eBay
Gazelle
ecoATM
Gizmodo