Months ago the idea of a "Global Name Registrar Contract" was thrown around. There is code to deploy one out there, but is there an official one that official clients (geth / Mist / etc) will use by default yet?
An Ethereum Request for Comment (ERC) titled "Default Ethereum Name Registrar" is on Github so it is in progress.
The primary author is Alex Van de Sande (email@example.com) who is employed by the Ethereum Foundation and is directly working on Mist.
There is EtherID which has 15k names/domains registered already.
It's a DApp by the way and works directly on your geth/eth client.
To enable it, run allow geth access by etherid.org like that:
geth --rpc --rpccorsdomain "http://etherid.org"
The most secure way to work with EtherID is through the mist browser. The developer pre-release is available here (v0.3.6).
Source code is available on github.
[Adding another answer instead of editing my last one, in case the "ENS" in my last answer is useful for historical reasons... ]
The Ethereum Name Service "...offers a secure and decentralised way to address resources both on and off the blockchain using simple, human-readable names."
The documentation, including an FAQ, can be found here: http://docs.ens.domains/en/latest/
Bidding on a name via an auction is covered in a previous question: How can I bid in an ENS auction?