If the software package you have came with the computer, then no you are not allowed to use it on another machine. If the computer had the operating system installed on it when you bought the machine (even if the disks are included) than it is considered on OEM licensing which mean it can only be installed on that machine and no other machines. If you bought the software box from Best Buy or wherever, you can install it on another machine. OEM licensing gets pretty tricky when trying to use on a different machine.
Carol: Brian is right. You can not use the XP restore CDs on a new Vista machine or even another XP machine. Most likely it will not even allow you to install it on another machine, but it definitly a violation of licensing. There are still computer companies producing machine with XP on them and you would be better going that route than than trying to remove vista and installing XP mainly because of the driver issues and some hardware on the new machine may not have drivers available for XP.