Some of the more interesting groups:
Adamites--supposedly went around naked.
Diggers--religious communists who tried to farm on common lands, hence the name.
Enthusiasts--a dirty word for anyone with strong feelings about religion. Or politics.
Family of Love--kind of like modern hippies (see previous post.)
Fifth Monarchists--wanted to turn the English government into a new Sanhedrin to usher in the Apocalypse. Actually convinced Cromwell to try the idea. No apocalypse happened.
Muggletonians--named Muggletonians. What else do you need?
And of course, there were some famous groups you've probably already heard of, like the Puritans and the Quakers.