From June 26th 2005 all visitors to the USA (traveling under the Visa Waiver Programme) will need a 'machine readable' Passport...
 
So how do you know if your passport is machine-readable?

There are two lines of letters, numbers and ´>´s printed at the bottom of the personal information page (the page with photograph and personal details). The text will be on a white strip on older machine-readable passports and directly on the pink page of newer passports. If there are no lines of text, the passport is not machine-readable.
The new 'Red' type with the data code below the picture.  
See these two pages for more info - 
The British Passport Service site.

The US Embassy London.