Are you planning to apply for a visa or are you planning to simply fill in the immigration card and omit to tell them about the offence. If your offence was involved with drugs or terrorism then the US authorities will be told by the English authorities and you will almost certainly be denied entry, and refused a visa if you apply. We share information with the Americans about this kind of thing. There is no obligation on the English authorities to give access to the Americans details of any other crimes, so unless you tick yes on the form that you have commited a crime, no one will bother to pursue it. From the beginning of next year anyone travelling to the US will have to give information three days before they travel, thus giving the Americans time to find out more about you, but they generally have better things to do with their time than go searching for minor offences and would probably not be able to get hold of the information anyway. They do not have access to our databases. How long ago was this offence, was it a major crime, bank robbery with violence etc, did you go to prison, was it all over the newspapers etc. I don't know anyone who has committed anything fairly minor bothering to get a visa, mostly they just tick no, no and no again on the immigration form.