(2-part post):
The rules on the US Embassy website state that anyone who ever been arrested or convicted of an offence is obliged to apply for a visa. The process is quite lengthy, involving getting hold of a copy of your police record from The Association of Chief Police Officers and attending an interview at the US Embassy in London. ACPO normally provide a Police Certificate within 10 working days. The current waiting time for appointments at the US Embassy is 15 days. The current processing time for visa applications is 4 days:
If US Embassy staff decide that your offence does not fall within the definition of 'moral turpitude' they have discretionary power to issue a visa. If your offence is classed as moral turpitude you will automatically be refused a visa. (Embassy staff have no choice in the matter. The US Immigration and Nationality Act bars you from entry). However you can then have your application passed to the United States Department of Homeland Security Customs and Border Protection, as an application for a 'waiver of ineligibility'. The MINIMUM processing time for such an application is 16 weeks. (There have been reports, here on AB, of some applications taking over a year to be processed).
US Embassy page:
http://london.usembassy.gov/add_crime.html
Statutory definition of 'moral turpitude':
http://www.state.gov/...rganization/86942.pdf