(2-part post):
The first point has to be that, irrespective of any criminal record, most UK citizens can't emigrate to the USA. To do so, you generally either need to have close family members there or you need to have professional qualifications to masters degree level. (You could also get in if you'd got skills which are in short supply in the US. Given their rising levels of unemployment, very few people can get a residence visa via that route).
See here for further information about US immigrant visas:
http://www.usembassy.org.uk/cons_new/visa/iv/i ndex.html
Next, a criminal record is for life. Within the UK, most criminal convictions become spent (for most purposes) after a certain period of time (which is defined by the sentence imposed). However, convictions never become spent when applying for employment which is exempted from the provisions of the Rehabilitation of Offenders Act. (e.g. when applying to work with children or vulnerable adults or for applications to join the police). Since the Act does not apply to foreign governments, convictions also never become spent when applying for visas to enter other countries.
See here for more information about the Rehabilitation of Offenders Act:
http://www.lawontheweb.co.uk/rehabact.htm