You can transfer your Google purchased domain name to another hosting service. Choose the host you want, e.g. GoDaddy, eNom, others, and get their steps for making the transfer. You will need to have your domain name unlocked and obtain the Authorization code from the current host.
If you are currently hosted by GoDaddy, log into your GApps Control panel, click on Domain Settings, then Domain Names. Next click on the Advanced DNS settings and sign-in to the GoDaddy DNS console using the Sign-in name and Password provided. Click the link for your domain name. You will see a link for
the Authorization Code: Send by Email. Click this and have the Code sent to you. You will also see a
line labeled Locked. If the status says locked then click on it and change it to unlocked. This is
very important for allowing the Transfer to occur.
If you are currently using eNom, you will not be able to get the Authorization Code or unlock your domain by signing into the Advanced DNS function for eNom. Instead you'll have to send an email to GoogleClients@enom.com. To see the typical response from eNom and what you will need to
do, see this thread:
http://groups.google.com/group/hosted-settingup/browse_thread/thread/f59bc8906d2f8eb3/f991977c3158b7c9?hl=en&utoken=Sm5HMzMAAABdyV45puCDqvZ6kZybelPyTrwW3sTr_SH3FM3gfEQcstTxrihkuw-pUAOmpHZGa-r0UEnFPSFW6wsHHKnE_us9
You may be limited by ICANN rules and can't transfer an account for 60
days after its creation or last move.
[Note to self: the following document contains the letter in the thread shown above just in case
it is no longer available: