Many alumni value continued access to their berkeley.edu email address as a way to identify themselves as Berkeley graduates. Communicating between alumni and using it for job searches are two common ways alumni use their accounts.
Things to avoid: Sending unsolicited email (SPAM) - even in relatively small numbers, sending SPAM can get your account blocked by Google. If your account is blocked, your account will be reviewed for abuse and can be subject to restrictions or revocation.
Using as a login to other services - Signing up...