This is a simple bash script that is run by crontab every 5 minutes on a linux box.
It e-mails me the new address when a change of IP address is detected.

The script (ipchangemail.sh)

#!/bin/bash 

# Check if IP-address has changed. If a change has occured, mail me the new address
# Add the following line to crontab if you would like it to be run every 5 minutes:
# */5 * * * * ./ipchangemail.sh

# The network interface I want to monitor
NET_INTERFACE=eth0

# File to keep the latest IP address
IP_FILE=myip.txt

# Mail to this address when a change occur
MAILTO=mail@example.com


# Read the previous IP address from file
source $IP_FILE

CURRENT_IP=`/sbin/ifconfig $NET_INTERFACE | sed -n "/inet addr:.*255.255.25[0-5].[0-9]/{s/.*inet addr://; s/ .*//; p}"`

if [ "$CURRENT_IP" != "$OLD_IP" ]
then
        # Send email about address change
        `echo "New IP address detected: $CURRENT_IP" | mail -s "New IP address" $MAILTO`

        # Write new address to file
        `echo "OLD_IP=$CURRENT_IP" > $IP_FILE`
fi

The script can be downloaded here.