You can do this, and use a tool called "sysprep" to remove any old machine identifiers. I added some instructions bellow.

Make sure you don't use the Administrator account as your main account as it looks like sysprep will remove it, causing you to lose all your files. After you run sysprep as bellow and the PC shuts down, remove the drive and move it over to the new PC. You will need to do a mini-setup of Windows as it will ask you for the key code, PC name, creating user accounts, etc... You will also need to make sure you have all the proper Vista drivers for your new computer to reload if needed.

You may want to backup your files to an external drive also to make sure nothing gets lost.

Sysprep.exe can be found in C:\windows\system32\sysprep\sysprep.exe. You will need administrative access to view/use this folder.

Sysprep does do some of its own clean up too. These are the things Sysprep will delete/remove:

• Deletes event logs
• Deletes restore points
• Disables the local Administrator account and deletes its profile
• Removes any SID information from the PC
• Removes any Plug and Play device drivers that were installed during initial installation of Vista
(these will automatically be re-discovered when the PC next boots up)

Once you have cleaned up your reference PC, it is time to run Sysprep. Sysprep takes less than a minute to run. All you do is open a command prompt, change directory to: C:\Windows\System32\Sysprep and type: "sysprep /generalize /oobe /shutdown"

The /generalize switch cleans up the PC - mentioned above.
The /oobe switch says to start the computer in Windows Welcome mode the next time it is booted up. The settings in your sysprep.xml file will be used to answer the questions that are normally entered manually during Windows Welcome.
The /shutdown switch shuts down the PC once Sysprep has run.

Note: Sysprep in Vista can be run with a GUI interface. Although generally, you would not do this, if you type just sysprep.exe with no switches at the command line, it will open a GUI version of Sysprep where you can check options for Sysprep.