The awsdd Python package allows you to use a free third-party public-IP lookup and a cheap Route53 zone to always keep your domain-name pointing to an accurate IP.

$ sudo pip install awsdd
$ awsdd -d <domain name> -z <zone ID> -a <access key> -s <secret key>
2014-06-15 12:09:30,836 - add.aws - INFO - IP update complete.

Now, add it to Cron.