(2-part post):
Does that mean me, Scoobydooby? ;-)
Posh123:
If you'd have posted your question before making an appointment at the US embassy, the majority of people, here on AB, would have recommended that you should simply 'forget' your convictions and enter the USA (illegally) under the Visa Waiver Program. The US authorities have no direct access to UK criminal records, so the chances of their immigration officials knowing about your convictions were effectively nil.
Now that you've decided to do things by the book, there's the possibility that (by booking an appointment at the embassy) you might have flagged something up in the immigration system so that US officials would be suspicious if you now tried to enter using a visa waiver form. So cancelling your appointment and 'chancing it' might now be riskier than if you'd not made the appointment in the first place.
The problem with trying to assess your chances of being granted a visa is that the US authorities don't provide an absolute list of what they regard as likely to cause problems. However, the visa waiver form (and other official US government publications) seem primarily concerned with crimes involving 'moral turpitude'. There's a definition of the term on the US immigration website but it's quite well summarised on Wikipedia:
http://en.wikipedia.org/wiki/Moral_turpitude
The definitions are possibly somewhat surprising. For example, some forms of assault don't come within the definition of 'moral turpitude' but simply nicking a Mars bar, for example, does.