No Serial Number in my Applecare Protection Plan box

If you bought it at the same time as the Mac, it is already registered to that Mac in Apple's database. So you don't need to do anything further.

When you order a computer from Apple with Apple Care, its serial number will be registered with Apple Care. You will receive an Apple Care certificate with the computer's serial number, and a box containing the Apple Care documentation and a CD with a limited version of Tech Tools. Since the computer is already registered, there is no need for an Apple Care serial number. There is no need to open the box since you can download a more recent version of its software through the Apple Care site. If you buy Apple Care from a store it will come with a serial number to use when registering your computer with Apple Care. This serial number can be used only once, but if the box is sealed, you know it hasn't been used. You were sold the wrong box.

Just purchased MacBook Air with APP. Found registration # in box. Process requires entry also of Serial#. Unable to log in for the APP does not recognize #'s. Is there a chance that the APP was activated already and I am unaware at purchase? Thanks.

If you have a AppleCare box that says "AUTO ENROLL", then, no worries, your Mac is already registered with AppleCare. If you have a #, then you'll need to register on AppleCare. I think this is it:

https://register.apple.com/cgi-bin/WebObjects/GlobaliReg.woa