Several accounts are for separating services - AWS has it's own account, for example, so does Dropbox. I use a different email address for forums and such.
A few for friends and family as well. --Friends I can tell to pay for themselves if I need to, but family, not so much.
Edit: As for checking them, most don't get many emails, and every good email app can handle multiple accounts easily, so I get notifications on my phone.
Fastmail allows you to do things like stavrosk@dropbox.yourdomain.com, and then you can filter emails by that domain name. Lets you easily block out spam without having completely different email addresses.
A few for friends and family as well. --Friends I can tell to pay for themselves if I need to, but family, not so much.
Edit: As for checking them, most don't get many emails, and every good email app can handle multiple accounts easily, so I get notifications on my phone.