I remember trying this when Apple's page first went live, but it said that my iPod Nano 1G isn't eligible. I, just now, submitted the serial number again, but now it says the following (I'll call them tomorrow to see if it really is or isn't eligible):
This serial number has already been submitted for this program. If you know you have not previously submitted this serial number for this program, please contact us.
I have a 2nd gen ipod nano... oh well. I think it still works. I also have a 6th gen 8 gig one and I have been using that. I'm glad to see that some are receiving new ones. I love Apple's support on replacement units, even if I'm not a huge fan of their OS. I do own an iPad and several iPods, and bought my daughter an iPhone 4 and she loves it.