Get your own domain through someone that has an email service that supports aliases. Every sign up can have a different address. It's like $10 per year and you're email is not at the mercy of whatever mega-corporation owns your email.
IMO, it depends on how many mailboxes and aliases you need. Providers like Fastmail charge by the mailbox (with up to 600 aliases for each). Same with Runbox, Mailbox.org, etc. (the number of aliases varies). Migadu provides unlimited domains, mailboxes and aliases for a fixed price that decides how many outgoing mails you can send everyday from all mailboxes in that account.
I use FastMail like this. They support both catch-all (comapny@domain.com) and user-specific forwards (company@user.domain.com -> user+company@domain.com) for domains with multiple users.
As the people above mentioned, look for one that supports a catch-all address. It makes it very easy to manage. You can even respond using a real "DoNotReply" account and the alias as the "replyto" address for the rare occasions you do want to reply. Yes, Google Apps does this well, but there must be others.
The percent of times I want to recieve email communication from something I have to sign up for is very close to 0.