Don’t you have an email acct. devoted solely to signing up for crap like this?
I have one and I just called it jem1234 ( jem stands for Junk E Mail) and anytime I come across some site wanting my email addy to get free goodies, that’s the address they get.
Once the coupon comes I just print it and delete. Once a month or so, I go into the acct. and just delete everything.
There are still lots of sites offering free webmail. Just sign up for one. And some of these sites will auto-delete any accts without any login from you in 30–45 days (or whatever limit they set).
Everybody should have at least one throwaway acct. you’d be surprised at how handy you’ll find it.