As you point out, there are several "classes" of email addresses that sites require, such as:
- One-time, or limited-time use where the email address is only used to access the information, but no email is actually sent.
- Sites where email is actually sent containing information, but this information is not considered sensitive (eg. social networking)
- Sensitive sites (online banking, etc.)
There are as many types of systems in the spectrum that you can think of. My personal system uses these three categories. You may also want to separate "sensitive" sites from actual correspondence with family and friends since breaches on their accounts can percolate to your own. Sensitivity of certain information may warrant their own email accounts.
One-time and limited-use sites use the email address as a login name only. Therefore use services such as 10minutemail.com to generate email addresses for their use. As long as you remember the email address name (or allow your browser to remember it), then you will not need the actual contents of the email account. Or generate a new account each time you need to access information.
Sites which will actually notify you -- and you want to be notified of events -- require an account that you can dedicate to that course. Create another account which you need not worry about. Make use of additional features, if they exist, such as gmail's "+" modifier to help streamline the process as required.
Sensitive sites are the email addresses you can carefully protect against giving out.
Placing these across several systems can help protect against a full breach.
Creating usernames which are uncommon or "random" can help prevent spammers with malicious intent from getting email to you by broadcast attempts. That is spammers may send emails to well-known first names, or well-known firstname/lastname combos) at domains to see if anything gets through (firstname.lastname@example.org or email@example.com). As with any security solution, obscurity is not security, but it can provide a veil of darkness that the average malicious user will have trouble penetrating.