CAUTION The answer about changing the UNIX password for "postgres" through "$ sudo passwd postgres" is not preferred, and can even be DANGEROUS!
This is why: By default, the UNIX account "postgres" is locked, which means it cannot be logged in using a password. If you use "sudo passwd postgres", the account is immediately unlocked. Worse, if you set the password to something weak, like "postgres", then you are exposed to a great security danger. For example, there are a number of bots out there trying the username/password combo "postgres/postgres" to log into your UNIX system.
What you should do is follow Chris James's answer:
sudo -u postgres psql postgres
# \password postgres
Enter new password:
To explain it a little bit. There are usually two default ways to login to PostgreSQL server:
By running the "psql" command as a UNIX user (so-called IDENT/PEER authentication), e.g.: sudo -u postgres psql. Note that sudo -u does NOT unlock the UNIX user.
by TCP/IP connection using PostgreSQL's own managed username/password (so-called TCP authentication) (i.e., NOT the UNIX password).
So you never want to set the password for UNIX account "postgres". Leave it locked as it is by default.
Of course things can change if you configure it differently from the default setting. For example, one could sync the PostgreSQL password with UNIX password and only allow local logins. That would be beyond the scope of this question.
Best Answer
There's the already mentioned pgsnmpd but it doesn't seem to be maintained actively (last release in August 2007). I'd rather recommend using the check_postgres Nagios plugin with the NRPE plugin of OpenNMS.