Yes, you can still buy a new PC with Windows XP installed on it. Windows XP ceased to be available at retail on June 30, 2008 but there are a number of exceptions. The relevant exception for a consumer or a small business owner is that "OEMs can downgrade Vista Business or Vista Ultimate licenses to Windows XP Professional or Tablet PC versions for customers indefinitely," where OEMs are the large PC manufacturers.
However, there’s a difference between "can" and "will" or "will with no hassle" so Christopher Null at PC World tried to purchase a PC with XP from Dell, HP, Gateway, Toshiba, Acer, Fujitsu, Lenovo, and Asus and reports on the very mixed results. Hit the article for the full details on each, but the best bets for an machine with XP preinstalled are:
Consumer PC: Toshiba, Fujitsu, Lenovo
Business PC: HP, Fujitsu, Lenovo
If you are willing to pay extra or install XP from a CD, the choices are even more numerous. Also Asus has its line of Eee ultra low-cost PCs (ULPC) which come with XP under a different exemption in the rules.