http://www.rewardsnetwork.com/earn/

I can't find a subprogram on their site that currently has an annual fee. But it seems that the cashback iDine subprogram has a lower cashback amount (topped out at 15%) than I remember it having when it had an annual fee, so it could be that they're experimenting back and forth with a program here or there (always with richer rewards than normal) that they might want to charge an annual fee for.

But not only don't they take the expiration date or the name on the card (there's no problem in my experience in registering a card that doesn't have the RN account holder's name on it), they let you register at least a dozen cards (at least in the airline dining programs). So which card would they bill? Obviously, they have to ask you which card to bill any annual fee for, get the expiration date, and get the name on the card (and maybe even a billing address, which again could be different than the mailing address you have on file at Rewards Network).