Having spent time working behind the Genius Bar, as a technician at an Apple Authorized Service Provider, and now as the owner of my own repair shop in Denver... I know the history of the replacement parts and where they come from. If you have been involved with Apple repairs, you will probably know what I'm reluctant to tell you. If you are merely a consumer, prepare to be disappointed.
The vast majority of parts that Apple ships to repair centers are what they consider "re-manufactured." As a Genius, I was coached to explain that process when we were asked where the parts came from. Customers would always respond with, "Wait, so you're giving me a refurbished iPhone?"
I was told to say no, and to follow it by saying, "re-manufactured parts or products are different than refurbished. Someone may have used your device before you if it's a refurbished product... but in the re-manufacturing process, Apple uses known-good parts and builds new units out of them." So, they added a fake, nonsensical name to pretend that their parts or products weren't refurbished.
What does this mean? The iPhone that you just received looks new on the outside because it has new glass, a new case, new battery... but the rest of the device is fair game for refurbished parts. The logic board, audio assembly, LCD, pretty much anything else on the inside that isn't visible from the exterior could be from another person's iPhone. I'm not saying that every part is used, every time... they'll use new parts if that's what they have in stock. But if they have working used parts, they won't hesitate to put them in your replacement iPhone. There is usually one scenario that will allot for a new replacement: if you purchased your device less than 14 days ago. In that case, they have the ability to do a POS (Point of Sale) swap instead of a repair. Any swap outside of 14 days needs a very good explanation and a manager's approval.
This doesn't just apply to iPhones and iPods; it actually applies to any part they put into your Apple product. The logic board they put into your MacBook Pro: refurbished. The optical drive they put into your iMac: refurbished. The DC-In Board they put into your PowerBook G4: refurbished. There are many, many parts out there that Apple will happily replace for you, but beware -- it's probably not new. Re-manufactured is no different than refurbished.
If you look at it from the environmental aspect, I have to give Apple some respect for repairing broken parts instead of just tossing them in the dump. Still, that doesn't mean that I -- as a consumer -- want someone's "fixed" two-year-old logic board going into my computer. At this point, though, I don't have much of a choice.