Most people simply 'forget' about their convictions and enter the USA under the Visa Waiver Program (with an ESTA). EU privacy laws bar member states from opening up criminal records, on a 'carte blanche' basis, to other governments. Only 'need to know' information (such as that relating to suspected terrorists, drug traffickers, etc) is passed on. The US authorities can make specific requests for information but they have to be routed through Interpol channels; they can't just ask the British authorities directly.
I've been posting that information (usually several times per week!) here on AB for the past few years but another contributor has recently provided a link to a response from the Home Office to a Freedom of Information request about what the UK authorities pass on to the USA. It confirms what I've been posting:
http://www.whatdothey...inal%20reply.doc.html
Chris