Technically you can already do this with gmail using the +tag trick, e.g. myemail+tag@gmail.com, where the "tag" can be the name of the website you are signing

Technically you can already do this with gmail using the +tag trick, e.g. myemail+tag@gmail.com, where the "tag" can be the name of the website you are signing up for. The emails will all go to your myemail@gmail.com account, but they'll be tagged with the tag.