Can a private key be copied to another machine?

[Larry Hanrahan]

Gnupg,

  I have a question concerning private keys.  I currently have a private
key on my laptop.  Can this same private key be copied to a desktop
machine and retain the ability to decrypt when I receive an encrypted
file or do I need to create a new private key and send the public key to
my various users?

  If this can be done, what is the process of copying the private key?

Thanks,
Larry