I want to make sure that the replacement iPhone I am being given is new, not refurbished.
Given the serial number, is there any way to tell if an iPhone is new or has been refurbished?
I don't think you can do it with the serial number, but if you were given a replacement in a box that looked like the original packaging, then it's new. Else it is a refurb — at least, that has been my experience with Apple so far. This thread also supports that:
So in short, if you're looking at replacing an iPhone just a few weeks or a couple of months after release, then it's most probably a new stock. If it's been a while since the model released, then it's most probably a refurbished phone.
There is no reliable way to figure it out.
It is entirely possible (not likely, but possible) that you could be getting a refurbished device, but it is more probable that its a brand-new device.
However, as I stated above, it is entirely possible that someone could have gotten a device less than a week old, returned it and it got a turn around.
Also, what you can do is look at the box when you do get it:
If its in the original packaging (e.g, black box with the iPhone on it), its new.
However, if its a plain white box, its a replacement. Replacements are traditionally packaged without any extras, although I did get earbuds and a sync cable in the one replacement device (iPod touch) I had to get from Apple.