Needing to connect via ssh to my work desktop from my home laptop, I developed a simple shell script that write IP information in a file and then send it by e-mail.
The execution of the script can then be scheduled with Gnome Schedule so that you are notified each time your external or local IP address changes.
sudo apt-get install sendemail
If your outgoing mail service requires identification I would recommend to install the gkeyring script, and copy it to the same directory as the whatsmyip script (last version available at https://code.launchpad.net/gkeyring/). This way you can use the gnome keyring to store your password instead of having it in clear text in the script.
To set it up:
./gkeyring.py -p whatsmyip=1 -1 -w PASSWORD