Even the Pilgrims were not always perfect "Christian angels". In fact, some racked up quite a criminal history. It could certainly be noted, however, that the Pilgrims who did rack up criminal histories all belonged to the London contingent, and were not the religious Separatists from Leyden. This list is not meant to be comprehensive.
1607: Mutiny on ship bound for Virginia. Sentenced to death, but sentence commuted on behalf of his wife and children.
1636: Assault and Battery of John Tisdale, fined £5. 40s.
1637: Disorderly Conduct: Allowing drinking and scuffleboard in his house on a Sunday, allowing servants to get drunk.
1638: Disorderly Conduct: Allowing three friends to get drunk at his house
1638: Price Fixing: Selling beer and nutmeg above the accepted price limit
1638: Breach of Contract: Failing to properly provide for his servant Dorothy Temple per his contract.
1639: Illegal Sale of Alcohol without a License
1621: Dueling. With Edward Leister. Sentenced, had heels tied to neck for one hour.
1633: Breach of Contract. With Joseph Rogers for failing to turn over six pigs
1633: Slander. Of William Bennett, fined 50s.
1634: Disorderly Conduct. Fighting with Josias Cooke and drawing blood, fined 6s. 8p.
1636: Assault. Of George Clarke, fined 10s.
1647: Theft. Stole wood from Samuel Cuthbert's land, fined 7s.
1650: Destruction of Property: Caused by his cows eating in a neighbors cornfield.
1621: Slander. Of Myles Standish. Sentenced to be bound heels to neck, but humbled himself before the governor and his sentence was commuted "it being his first offense".
1624: Conspiracy. Implicated in the Oldham/Lyford scandal, but found not guilty due to lack of evidence.
1630: Murder. Of John Newcomen, sentenced to death and hanged in September.
1638: Breaking the Peace: Illegal entertainment of John Phillips.
1638: Public drunkenness.
1645+: Polygamy. Was a seaman who had a wife on both sides of the Atlantic. Unknown to the Court, so never charged.
1688: Adultery. Excommunicated by church, but not charged by Court for lack of evidence. Sought forgiveness in 1691, and was re-admitted to church.