Just to add to the (entirely correct) posts from LCDMAN and Dzug2:
The UK's Rehabilitation of Offenders Act isn't recognised by the US authorities. (i.e. offences can NEVER become 'spent' when seeking to enter the USA).
Anyone who ever been convicted of a crime (with a few very minor exceptions) ceases to be eligible for a visa waiver. You must apply for a visa.
The first thing that the US Embassy has to consider is whether the crime was one of 'moral turpitude'. If it's not, Embassy staff MAY decide to grant a visa (although they refuse a great many applications). However if the crime involved moral turpitude, the Embassy staff MUST refuse a visa. (They have no choice. It's written into US law). At that point though, the application can then be referred to Washington as an application for a 'waiver of permanent ineligibility'. If such a waiver is granted, the Embassy can once again consider the visa application.
Even if the crime didn't involve moral turpitude (so that no referral to Washington is involved) the process is quite lengthy. (You must get hold of a copy of your 'police record' and send it, with the forms and the not-insubstantial fee to the Embassy. You then have to get an appointment to attend an interview in London, for which there's usually a wait of at least several weeks. Then you have to wait to here the outcome of your application. If it's refused, you lose your fee).
So the simplest procedure can take several months but, if a referral to Washington is involved (because of 'moral turpitude', it can take far longer. (Someone posted here to say that her husband waited 15 months, only to have his application refused through two counts of driving without insurance).
The definition of moral turpitude is very broad. For example, ANY theft (e.g. nicking a single sweet from the pick-&-mix counter) constitutes moral turpitude. The official definition of moral turpitude is contained within this document:
http://www.state.gov/...rganization/86942.pdf
Chris