It is a good idea to save the database server's log output somewhere, rather than just routing it to /dev/null. The log output is invaluable when it comes time to diagnose problems. However, the log output tends to be voluminous (especially at higher debug levels) and you won't want to save it indefinitely. You need to "rotate" the log files so that new log files are started and old ones removed after a reasonable period of time.
If you simply direct the stderr of the postmaster into a file, you will have log output, but the only way to truncate the log file is to stop and restart the postmaster. This may be OK if you are using PostgreSQL in a development environment, but few production servers would find this behavior acceptable.
A better approach is to send the postmaster's stderr output to some type of log rotation program. There is a built-in log rotation program, which you can use by setting the configuration parameter redirect_stderr to true in postgresql.conf. The control parameters for this program are described in Section 17.7.1.
Alternatively, you might prefer to use an external log rotation program, if you have one that you are already using with other server software. For example, the rotatelogs tool included in the Apache distribution can be used with PostgreSQL. To do this, just pipe the postmaster's stderr output to the desired program. If you start the server with pg_ctl, then stderr is already redirected to stdout, so you just need a pipe command, for example:
pg_ctl start | rotatelogs /var/log/pgsql_log 86400
Another production-grade approach to managing log output is to send it all to syslog and let syslog deal with file rotation. To do this, set the configuration parameter log_destination to syslog (to log to syslog only) in postgresql.conf. Then you can send a SIGHUP signal to the syslog daemon whenever you want to force it to start writing a new log file. If you want to automate log rotation, the logrotate program can be configured to work with log files from syslog.
On many systems, however, syslog is not very reliable, particularly with large log messages; it may truncate or drop messages just when you need them the most. Also, on Linux, syslog will sync each message to disk, yielding poor performance. (You can use a - at the start of the file name in the syslog configuration file to disable this behavior.)
Note that all the solutions described above take care of starting new log files at configurable intervals, but they do not handle deletion of old, no-longer-interesting log files. You will probably want to set up a batch job to periodically delete old log files. Another possibility is to configure the rotation program so that old log files are overwritten cyclically.