Just a little touch of whitewash and favorable editing of historical memory there, Gray.  I had ancestors, not on the Mayflower but on one of the shortly following ships to the Mass.Bay colony.  Religious 'freedom', as we think of it now, was definitely NOT on the agenda.  What the Puritans wanted was the freedom to practice *their* version of christianity w/o State prosecution - and it fairly rapidly became apparent that that included the 'right' for their church and local/village gov'ts  [pretty much 1 and the same] to deal w/'unbelievers' in any way the 'rightous' saw fit - often as, or more, brutally than they had been dealt w/in England.  
Some other colonies were catholic or church of England - but rather more  indifferent to an individual's religious persuasions [it was hard to be Less tolerant than the New England States].  Other colonies were just generally protestant, or largely commercial and indifferent.