Throw away his old phone, mail it to him, or return it to the cell phone provider. There's no reason for you to be reading his emails.
Lest I sound holier than thou, I did the same thing when my last ex left his email account open, to which I had access on my computer. I actually emailed some woman he was talking to, to inform him he was a liar (he wasn't cheating, this was after we split up). It made me feel creepy and I told him to close the account.
I get the temptation, but no good ever comes of it. Ever.