My oldest unread email is from May 8th. I tend to skim through the subject lines and if it doesn't seem important, I will just skip it. Most of my unread emails will go directly into the trash as they are just FYI transmittals which are sent to everyone whether they need it or not. Unfortunately, this leads me to days where it will take me several hours to clean-up messages and actually delete them.
Once in a while I will find an email from a week or so in the past that seemed urgent at the time but managed to work itself out by the time I read it.