That depends on the country in which you live.
Look it up:
In the U.S
If you own an iPhone that is ineligible for warranty service but is eligible for Out-of-Warranty (OOW) Service, Apple will service your iPhone for the Out-of-Warranty Service fee listed below.
iPhone model Out-of-Warranty Service iPhone 5 $229 iPhone 4S $199 iPhone 4, iPhone 3GS,
iPhone 3G, Original iPhone
A $6.95 shipping fee will be added if service is arranged through Apple and requires shipping. All fees are in U.S. dollars and are subject to local tax. "
Apple doesn't do trade ins, though, in some places they work with companies who do. Broken phones don't generaly garner much. You might be better off selling it for parts. Depending on what is wrong with your phone, you may be able to get an out of warranty replacement which would require you turn in the old one.