I sign up with a different email address on every website. (I have a catchall at my domain, rather than using plus-addressing.)

The results are more boring than you think. Almost no one leaks my address. A couple have been hacked, but almost all of those are widely known. (I did discover one early and help Troy Hunt validate a leak.) At least one Kickstarter campaign has shared my address, as has a local business. But that seems to be the extent of it.

I still do it, because I did manage to catch those things, and because it reduces cross-site correlation. But yeah, there's less skeevy behavior than you might think.

mailbox.org hooked up to Thunderbird allows you to do so using custom domains. You can send and receive email as any string @ your domain.

You can do something like [email protected] and it'll be delivered to [email protected] with the site in the To field