After watching the finale of Game of Thrones, I wonder if human cultures have ever had a history of punishing people through walks of shame or atonement. Did these ever actually happen? If so, for what reasons and what were they like?
Medieval and later Europe did a lot of that.
Your Spanish auto da fe was a grand procession of penitents, garbed in a code to designate their sins, surrounded by guards, to the plaza. Some were let off with the public shaming, some were whipped or branded, some were burnt at the stake.
The punishment for prostitution was often being stripped to the waist, hands tied to the tail of a cart, and, while the cart rumbled down the street, being whipped by the apprentice executioner following along. A woman who fell down or tried to stop would be dragged behind the cart (which travelled at a slow walk). This is through the 1700s.
More often, because of the rowdiness of the mob, malefactors would be drawn in a two-wheeled cart to the place of punishment. They were made to stand, and the crowd would throw the usual rotten produce and dead small animals at them as they went along. It's said that for aristos going to the guillotine in The Terror, the humiliation of the trip made death a relief.
Just a quick answer b/c I'm on mobile, but the shaving of heads of women who slept with Germans during the war is one such act, although I'm not sure they were ever stripped first.
In 1863 a 15 year-old girl named Osichi purposefully set fire to part of Edo, present day Tokyo. Allegedly, she was trying to burn down her house (she didn't intend it to spread beyond her quarter) so her family would be evacuated to a temple where she was supposed to meet her lover. Once she was found guilty, she was paraded from Yotsuya to Asakusa, roughly a two hour long walk, before she was crucified. She probably had to do it barefooted, and people were watching, but I'm pretty sure that was it. She became quite a popular figure in Japanese in kabuki plays, Edo period fiction and the like.