This is the cheapest of cheapo you will find for a script that performs remote backups using simply rsync, a destination host, and a directory on that destination host to store the backups.

cheap_rsync.sh

#!/bin/bash
#
# Cheap Rsync System for Remote Backups
#
# This is the cheapest of cheapo you will find for a script
# that performs remote backups using simply rsync, a destination
# host, and a directory on that destination host to store the backups.
#
# Author: Jason Gegere
# Date: 11-21-2006, 9:29AM CST

#################
# CONFIGURATION #
#################
ADMIN_EMAIL="email@example.com"
BACKUP_DIRS="/home/cheap_rsync4/beta2/"
MY_HOST="beta2"
DESTINATION_HOST="host.domain.com"
DESTINATION_DIR="/var/dev/$MY_HOST/"
BACKUP_USER="cheap_rsync42"
BANDWIDTH_LIMIT=3047      #In Kilobytes

###################
# EMAIL PROCEDURE #
###################
bad_email() {
        echo "A backup failed on $MY_HOST while attempting to backup $1 over to $2:$3" | mail -s "Cheap Rsync - BACKUP FAILURE - $MY_HOST" $ADMIN_EMAIL
}

##################
# MAIN PROCEDURE #
##################
backup_main() {
        echo -e "Preparing to backup directories ...\n"

        for Dir in $BACKUP_DIRS; do
                echo -e "Backing up '$Dir' to $DESTINATION_HOST:$DESTINATION_DIR ..."
                if [ -d $Dir ]; then
                        echo -e "Running rsync command ..."
                        lstat=`rsync -rtavze 'ssh -p 22' --delete --numeric-ids --bwlimit=$BANDWIDTH_LIMIT $Dir $BACKUP_USER@$DESTINATION_HOST:$DESTINATION_DIR`
                        if [ "$lstat" = "" ]; then
                                echo -e "There was a problem rsync'ing $Dir!"
                                bad_email $Dir $DESTINATION_HOST $DESTINATION_DIR
                        else
                                good_dirs[${#good_dirs[@]}]=$Dir
                        fi
                else
                        echo -e "$Dir is invalid, unreadable or not a directory!"
                        bad_email $Dir $DESTINATION_HOST $DESTINATION_DIR
                fi
        done;

# if [ ${#good_dirs[@]} -gt 0 ]; then
# echo -e "Backups were successful on $MY_HOST:\n\n${good_dirs[@]}" | mail -s "Cheap Rsync - BACKUP COMPLETE - $MY_HOST" $ADMIN_EMAIL
# fi
}

backup_main