An email address must not exceed 254 characters.
This was accepted by the IETF following submitted erratum. A full diagnosis of any given address is available online. The original version of RFC 3696 described 320 as the maximum length, but John Klensin subsequently accepted an incorrect value, since a Path is defined as
Path = "<" [ A-d-l ":" ] Mailbox ">"
So the Mailbox element (i.e., the email address) has angle brackets around it to form a Path, which a maximum length of 254 characters to restrict the Path length to 256 characters or fewer.
The maximum length specified in RFC 5321 states:
The maximum total length of a reverse-path or forward-path is 256 characters.
RFC 3696 was corrected here.
People should be aware of the errata against RFC 3696 in particular. Three of the canonical examples are in fact invalid addresses.
I’ve collated a couple hundred test addresses, which you can find at http://www.dominicsayers.com/isemail