Sorry for necro-posting ... but in case someone finds this via Google just as I did, I'd like to add this little bit:

I am a Dropbox user ... and Dropbox also exists for iPhone and Android phones ... so why not use Dropbox to record the external IP address? I could then check the IP via the web interface, or via my iPhone, or via any of my other computers that I sync with. Sounds like a good idea, doesn't it?

Based on the previously made suggestions by all the other posters here (thanks guys!) I have added this nifty little cronjob to one of my "green PC's" (it only consumes around 10 Watts) that is constantly running, so it's a good candidate for this job:

 */15 * * * * /usr/bin/wget -O - -q > /home/YourUserNameHere/Dropbox/ExternalIP/`hostname`.txt
So this cronjob will run every 15 minutes and then output the external IP the system sees into a file that is located inside my Dropbox folder. The file will be named after the hostname this cronjob is running from.

So I could have this cronjob on multiple systems and they would all report their external IP address back to me, no matter where they are.

I hope this will be useful for anyone who finds this via Google ...