The 'official' answer (based upon what's on the US Embassy website) is that anyone who has ever been arrested, convicted of a criminal offence or has simply admitted to committing one is ineligible to enter the USA under the Visa Waiver Program, i.e. with an 'ESTA' (= Electronic System for Travel Authorization).
Since a police caution can only be given if the offender accepts it (which is effectively an admission of guilt), and that caution would probably have followed an arrest anyway, that means that (according to the rules) anyone who has received a caution can't use an ESTA and must apply for a visa.
The visa application process is long and tedious, involving obtaining a copy of your police record and attending an interview at the US Embassy. If the relevant offence involved 'moral turpitude' (which includes all types of theft, even simply nicking a Mars bar) or drugs, US law requires that the Embassy MUST refuse to issue a visa in the first instance. The application can then be forwarded to Washington as a request for an exemption from the bar upon entry. The standard visa application process can take several months but if a referral to Washington is required, the MINIMUM processing time is around 5 months (with a delay of 15 months having been reported here on AB).
As others have suggested, simply 'forgetting' about a caution is probably the best course of action, as it's extremely unlikely that the US authorities would get to know about it. However if they did find out you'd be refused entry. (Nigella Lawson was refused entry solely because she'd admitting to using cocaine, even though she'd not been arrested, cautioned or convicted of any offence).
http://london.usembassy.gov/niv/add_crime.html