Oh man, what a great idea. Especially as you start shopping around, you can build a broader profile of a customer's shopping habits, which could be sold for better targeting advertising.... oh wait... argh why does my mind always go there.
On the backend it can solicit better offers from other merchants on the same and similar merchandise.
Also, as you note, the customer's data could be sold and (partially) turned into a rebate. Perhaps the site could also tell you which extra data (your gender, age, other purchases, etc) would be the most valuable and you could choose to release these facts.