There was a $200 sign-up bonus a year or so ago, as they were phasing out the Discover More card.
If you sign up for a Discover through Amazon's credit card section, you get a $75 Amazon gift card on first purchase. Then after your first purchase, Discover tells you it takes 8 weeks to mail you the gift card.
I just got a Discover card through Amazon because it has even better shopping protection features than AMEX, e.g., price protection, purchase protection, return protection...
It's main purpose in my wallet is for large electronics, appliance, or other big purchases like that I want the warranty extended on, etc.. I'll look at the rotating categories every 3 months and see if I'm interested in using the card for one of those.
The thing is, I think in general, you don't get as good a sign-up bonus for cards that don't have an annual fee, especially not for cards that don't have an annual fee and have great features.
Discover is going more for long-term customers than people who are drawn in by a big sign-up bonus.