Most systems have the logger utility, which knows how to talk to syslogd. It allows you to set log level (severity), facility name, specify the log file to write to, send to syslogd on a remote host, write messages to STDERR as well as to the system log.
The logging semantics are not quite the same as those provided by tools like log4j, but by combining the facility.level settings with message tags, you can achieve something very close.
Examples
NOTE: These examples use the FreeBSD version of logger. Your system may have different options, so read your local documentation!
logger -p local3.info -f /var/log/messages -t MY_LOG_TAG "something interesting happened"
This will send the message to be logged in /var/log/messages with a severity of info, in the local3 facility. It includes a tag (-t MY_LOG_TAG), which is included in each line. Tags are useful for extracting log entries with grep, awk, etc.
logger -h loghost -p mail.crit -s -f /var/log/mail "an unrecoverable error has occurred"
This one sends the message with severity crit in the mail facility to the remote machine loghost, to be logged in /var/log/mail. The -s causes the message to be printed on the the script's STDERR as well as sending it to be logged.