The above are correct... though there are some loopholes.
If the iPod is unregistered you can call Apple and explain that you got it as a gift with no reciept and would like to buy AppleCare for it. They'll be flattered that you're both so well informed and that you took the time to call them. Register the AppleCare and the iPod at the same time. This should get you the full Warranty period from the point of your registration.
Apple can research the sale of a Mac or iPod only as far as the retailer that sold it without the Registration having been filed electronically. Often they can't even verify it's been sold unless the reseller is particularly vigilant about relaying it's serial #'s from sales records to Apple... very few are.
If, by some twist of fate you CAN'T get Apple to register your product with the full term on the Warranty or to sell you AppleCare (extremely unlikely) you can get ServiceNet through their (servicenet's) webstore. I have had mixed success with them but they'll Warranty nearly anything.