RFC 3696 says that the maximum total length for an email address is 320 characters ("local part": 64 + "@" symbol: 1 + "domain part": 255 = 320). It's very rare that you'll encounter an address this long, but you should support them nevertheless.
Source: https://www.rfc-editor.org/rfc/rfc3696 (section 3: Restrictions on email addresses, last paragraph)