Maybe.
To install XP, you have to first Vista. That can only be done by deleting the partition that holds Vista and creating a new one. That means that anything you have stored on the computer (music, pictures, etc) will be permanently wiped and extra programs that came with the PC will be gone.
Before installing XP, you will need drivers for the video, audio, network card, modem, etc. Otherwise you will lose your sound, Internet and only have a poor picture. If it is a new computer there may - or may not - be XP drivers. No drivers, you can not use XP. (If it is a laptop, odds are 99% that there are no drivers.) Check the web site of PC's manufacturer to see if they have XP drivers.
Realized that Microsoft is no longer selling XP. Good luck getting a copy. Microsoft has also dropped support for XP. This means that the next time a bug or security hole is found in XP (average being about once a month), Microsoft will no longer be pushing out updates to fix it. It could leave all XP computers wide open to hackers and viruses.
Also as Vista and Windows 7 are very very different in the type of hardware and software they need, most manufacturer's are no longer designing their programs, games, and hardware to be backwards compatible with XP. Six months from now you will not be able to buy anything that will work with XP. It is a dead OS, let it rest in peace.
If you do not want Vista, then wait a few days for the release of Windows 7, and take the same money you would have to spend on XP and purchase a Windows 7 upgrade instead. You can install it without having to wipe the computer, and be going ahead to the latest OS that will be valid for the next 5-7 years, instead of backwards to a dead, unsupported OS.