Most (Western) Europeans can enter the US on the Visa Waiver program. That gives you 90 days. Any longer and you need a visa.
If you have any criminal record (e.g. a DUI, caution for possession of pot etc) you become ineligible for the visa waiver program and should apply for a visa and your local embassy. That's regardless of whether the offence has expired and been purged from your record at home. In theory, the US has access to the UK (and presumably other counties') criminal records to check this, but as most UK police forces can't put together a complete criminal history of a given person, the US authorities have no chance. In most cases, it is unlikely the checks ever take place and I know several people with minor offenses enter under the visa-waiver program without a problem.
The US VISIT stuff (finger printing and photographing) at the airports isn't that big a deal - most airports are pretty slick at the process and it really doesn't bother me. I have to admit it did piss me off to start with though, but hey - it your country, your rules.
And the end of the day though, as we all know - official legislation makes he-haw difference to the US's ability to keep out undesirables of any nature. I'm still here and my wife tells me I'm undesirable all the time...