Can I move an xbox live Gold account to a different xbox?

Yes, you can pretty easily move your account, which is linked to your Gamertag and gamer profile. If your profile is saved to an Xbox hard drive, you can directly move that hard drive to the new Xbox. Same if it's on a memory card or USB memory stick.

If the old Xbox is a complete loss, you can still recover your Gamertag from Xbox Live. See the following article for details: http://support.microsoft.com/kb/907333

An important note about all these is that your gamer profile can only exist in one location, with a backup on Xbox Live (which is what you recover, using the above method).

Good luck and good gaming!

yes either switch hardrives or memory cards or use a cable to switch info and data from one hardrive to another but the easiest thing to do is switch hardrives or memory cards depending on what u have