Did any actual Puritan congregations impose scarlet letters on adulterers? Nathaniel Hawthorne's (fictional)  book, the Scarlet Letter, in my opinion, has seared a characterization in people's minds that Puritans were dour, hypocritical, legalistic, and shame-driven Christians. Having read many of the actual writings of the Puritans, this characterization seems completely foreign, almost to the point of thinking that Hawthorne was deliberately inventing a horrible community so he could drag the Puritans down.

Are there any real historical examples of scarlet letters (figuratively or literally) on sinners for their sins?

It is hard to imagine that the religious movement that produced Richard Baxter (himself a notorious drunk before conversion), Hugh Binning, John Owen, Jonathan Edwards, or Jeremiah Boroughs would be associated with something as antithetical to their doctrine as the public shaming of notorious sinners as a form of penance.
I found only one instance of where a woman caught in the act of adultery was forced to wear the letters AD round her neck.  Whether this punishment was imposed on her by the Puritan congregation, or by the Court, I don't know.  However, that seems to be getting off lightly!

In 1631 the Massachusetts Bay General Court declared adultery a capital crime. Mary Latham, only 18 years old when she married a much older man, was executed for adultery.  She was convicted for committing adultery with one man and then confessed to having sex with 12 others. 


  “The woman proved very penitent, and had deep apprehension of the foulness of her sin, and at length attained to hope of pardon by the blood of Christ, and was willing to die in satisfaction to justice. The man also was very much cast down for his sins, but was loath to die, and petitioned the general court for his life, but they would not grant it...  They were both executed, they both died very penitently, especially the woman, who had some comfortable hope of pardon of her sin, and gave good exhortation to all young maids to be obedient to their parents, and to take heed of evil company."


http://www.eyewitnesstohistory.com/adultery.htm

In 1639 Mary Mendame was found guilty of committing adultery with an Indian man; she was whipped at a cart's tail, which meant she received a whipping while the cart was being drawn through town.  Her lover was "only" whipped at the post, a lesser punishment than the whipping she received at the cart's tail, because the judges said she had enticed him.

In 1641 Anne Linceford confessed to committing adultery and was punished by "an immediate severe whipping at the public post in Plymouth [and] a second whipping at the public post in Yarmouth [where the act was committed]," according to "Sexual Misconduct in Plymouth Colony." She also had to wear the letters "AD" on her clothing from that point on.

Married men who had sex with a single woman were charged with fornication, while married women who had sex with a single man were charged with the more serious crime of adultery.  You might find the information in this link helpful, part of which says: 


  “Fornication was by far the most common sexual offence to come before the Plymouth courts. Between 1633 and 1691, sixty nine cases of fornication were presented. I include "carnal copulation," "uncleans," and births of illegitimate children with fornication. The enactment of 1645 that outlined the punishment for crimes of fornication distinguished between acts committed before and after the time of marriage contract. The fine for fornication after contract was only five pounds per person -- half the fine for fornication before contract. Interestingly, only four of the sixty nine cases clearly occurred during the period of marriage contract. The chart below shows the percentages of fornication cases that occurred during the period of contract, before contract but between couples who eventually married, and completely outside of intended wedlock. The split between eventually married and never married couples is a near fifty-fifty division.”


http://www.histarch.illinois.edu/plymouth/Lauria1.html