Google has partnered with GoDaddy.com and eNom for domain registration services with its Google Apps for Your Domain product:
To offer users without a domain an easy way to find, register, and buy a domain and start immediately using our services. When you register a new domain as part of the sign-up process for Google Apps for Your Domain, we'll work with our partners behind the scenes and automatically configure everything so it works with all of the services available through Google Apps for Your Domain right out of the gate. We also give you full control of your domain settings, so you can use your domain for other services not provided by Google.
We are offering domains for $10 per year, which includes private registration.
The Google Apps for Your Domain FAQ indicates:
Google doesn't register or host domain names. We've partnered with a few companies that offer these services because it's a lot easier to set up a Google Apps for Your Domain account this way. If you'd like to access your hosting account, click Advanced DNS settings in your control panel. You'll be directed away from Google.
To set up Google services at your domain and customize the URLs for login pages, you won't need to visit your hosting account. But, if you'd like to access these records, we're providing an easy path through the control panel.