Travel to the USA?

I have a holiday booked in December to New York and am worried that i may need to apply for a visa? About 9 years ago i was verbally cautioned for shoplifting, the police advised that this would not show on my recored after 3 years. Even though I was not charged and have nothing on my record will I still need to apply for a visa?
I am travellijg from the UK and do not have a current visa

it all depends on which country you are coming from and if your old visa expired

Have a look at the offical site for the US Visa Waiver Programme. That should give you the info you need:

http://travel.state.gov/visa/temp/without/without_1990.html

The USA (for some god forsaken reason) has the Visa Waiver Program for most European countries, UK included. Which means you can enter the US on business or pleasure only for 90 days. After 90 days you must depart to your country, in other words, as a good rule of thumb, not a country that is within 5 hours of flying distance to the United States. However, if this charge is on your record the Immigration Officers will know and might discuss it with you. Usually a small charge like that is no big deal, but then again we (the USA) don't know if you'll do it again. Not saying that you will.

How long are you staying in the USA? If it's just a short period (vacation) I don't see why you would be required to get a visa, your passport should be fine. Visa is for extended stay, but check just to be sure.

As far as the shoplifting warning and the 3 year record...Don't really know what was meant by that. If you got caught shoplifting and NYC police got involved your name is on an incident report somewhere in the records department of the NYPD. I seriously doubt anyone will find it, or look for it, or care about it.