I go with "I don't share that information," on that one, personally.
I have heard both the "What's your email?" and the "Would you like to sign up for <stuff> with your email?" and other permutations. It's similar to the way a lot of places would ask for a phone number, and the answer was the same then: "I don't share that information."
They used to ask the latter (phone number) regularly at one place we shopped a fair bit, and asked: "So... why are we constantly being asked this? It's invasive." The salesperson sighed and nodded and actually knew what they were using the info for at the time, for their store, and she told us. They send out mailers regularly, and before they had custom UPCs that would mark which address that particular mailer was being sent to (which they apparently do now, similar to the custom 'text it to yourself' coupon things some retailers use now on websites), they used that information to geographically track which local areas had the highest customer concentration. The end result in that case is relatively harmless, but once they have that information, they can do anything in the world with it -- it's not like they get rid of it, so even if they only use it for that focused and harmless purpose today, tomorrow might be different.
We're seeing the email tracking now in part due to the volume of mobile phone use, which makes geographical tracking by phone number a lot less reliable. (My husband and his mother share an account; they both have New Jersey numbers while he lives in DE and she lives in FL, for instance, and a fair number of the folks I know have mobile numbers in a similar position if they've moved and kept the number, etc., which a lot of folks do.)