Hi Scott,
I'm no expert but here's one way (not necessarily elegant).
In the following example,
eth1 is my external interface
someone@somedomain.com is the e-mail you want to send the notice to
Create a script file (eg. mailIP) with this command line :-
ifconfig eth1 | grep -i 'inet addr:' | mail -s 'IP Address' someone@somedomain.com
Then create a cron job for this script at the appropriate interval.
This will e-mail someone@somedomain.com with a message with the subject "IP Address" and contains a line like this :-
inet addr:aaa.bbb.ccc.ddd Bcast:255.255.255.255 Mask:255.255.255.0
(Sorry, don't know enough commands to just filter out everything but the IP address. Anyone who can further refine this, please do so as it would be good to learn some new commands).
Kelvin