How to create a custom dynamic DNS solution?

You all probably know commercial dynamic DNS providers like dyndns.org or no-ip.com. But how to create a similar service for just a handful of machines? What server software would be best suited for such a setup (under Linux)? Advantages: - the service would be under your control - no tracking by some opaque company Minimal requirements: Probably something like: you own at least one host machine with a static IP, a domain and your domain provider let you configure DNS records. Clients: A few machines that are connected via cable/DSL and only get dynamic IP addresses on each dial-up and/or every x hours.