Officially (i.e. according to the rules on the US embassy website), anyone who has ever been arrested (even if totally innocent) or convicted of any offence (other than minor, non-arrestable motoring offences) must apply for a visa.
Whether you decide to 'do things by the book' or 'chance it' (and enter under the Visa Waiver Program) is up to you.
Chris, since this is apparently asked several times a day, fancy doing a kind of composite reply as a post, and then just posting the link to it each time?
i know someone who had a dope conviction and when he got to the US he was denied entry. This happened several years ago, so i'm surprised their systems were so sophisticated back then. Maybe he told them, but i doubt it.