I have a Gmail for communicating with actual people, and some important stuff like banks, Facebook and whatnot. I keep it clean of unread mails and generally check everything I get immediately. I do a "select all -> archive" every once in a while to keep the inbox nice and tidy, too. I don't usually label stuff manually but I have some filters set up to label some things automatically.

Then I have an account at mail.com which I use for 99% of signup forms and newsletters and whatnot. I don't check it frequently at all - maybe once a week, when I just skim the subject lines and check what interests me, then I select all and mark as read.

It makes for very unobstructive email interaction!