[ceol]

If you have a dynamic IP, Dyn offers DNS services[0] that let you tie a domain to it through them. I believe it requires you to install something on your machine that monitors your IP and reports it back.

Otherwise, you just use your IP and make sure to edit the DNS yourself when it changes.

[0]: http://dyn.com/dns/

[Stratoscope]

Many routers have dynamic DNS support built in now. For example, my Asus RT-N66U supports several DDNS services including Dyn and a free one that Asus provides for its router customers at {yourcustomsubdomain}.asuscomm.com.

No big surprise here, since the router is really just a nice little Linux box.

[ceol]

Ah, I have an Asus RT-N16. DD-WRT is truly awesome!

[kysol]

That would be something like: http://dyn.com/support/clients/linux/ddclient/