In Germanic folklore, St. Nicholas is often accompanied by Knecht Ruprecht, a sort of servant who gives out punishments to naughty children. This is often in the form of lumps of coal, rocks, and sometimes even leaving behind a switch or stick for their parents to use for disciplining them. Knecht Ruprecht is so widely known that in the German version of The Simpsons, their dog is named Knecht Ruprecht, which is a substitute for the name "Santa's Little Helper."
The Krampus is a demonic anti-Santa who roams the night the evening before the Feast of St. Nicholas, looking for naughty children to devour. If you're trying to get your child to sleep so that St. Nick can visit, telling them a minion of Satan is also stalking the night at the same time doesn't seem like the best strategy.
Australia has long been known as a rugged country, so it makes sense that Santa would need to upgrade his gear for the trek. In Australia, Santa's sleigh is pulled by six white boomers, or kangaroos. Their names are Jackaroo, Bluey, Curly, Two-Up, Desert and Snow. The kangaroos are said to be stronger than reindeer, which is why he only needs six instead of eight (or nine if you're counting Rudolph).
In Russia, the yearly gift-giver is known as Ded Moroz, or "Father Frost." He is often accompanied by his granddaughter Snegurochka, or "The Snow Maiden." Unique to Ded Moroz is that he and Snegurochka deliver presents in person. There's no sneaking into a house with these two. Ded Moroz visits are usually arranged in public places around New Year's Eve.
In the 19th century, gifts were brought to Scandinavians via the Yule Goat, a man-sized goat usually portrayed by the man of the house in a costume. Modern interpretations like the one pictured above use the Yule Goat as an ornament made of twigs or straw, since Santa Claus is now known there.
Similar to the Yule Goat, Joulupukki was originally a goat man who went door-to-door demanding food, drink and other gifts during the holiday season. Somewhere along the line he was converted into Finland's version of Santa Claus, and he now delivers presents by knocking on the door during Christmas Eve celebrations. Interestingly enough, Joulupukki's reindeer do not fly, but pull his sled the old-fashioned way.
Catalonia is a region of Spain encompassing the entirety of Barcelona, among other cities. Around Christmas time, it is full of people who pray for a log to, uh...excrete candy. Yeah, you read that right. The Tio de Nadal is a log with a happy face that is placed in the fireplace or center of the living room, wrapped in a blanket and beaten with sticks. Then the children leave the room to pray for it to poop out candy, and while they're gone, the older family members place the candy under the blankets. This process repeats until it is out of candy, which is signified by the log leaving something unpleasant behind such as garlic, onion, or fish.
In the Czech Republic, Jezisek is a child version of Jesus who delivers presents. The children who receive presents from Jezisek actually open them on Christmas Eve rather than Christmas Day. Unlike Santa, Jezisek enters the house through open windows and sets up the family Christmas tree.
In Italy, La Befana is an old woman who delivers gifts around Christmas. She shares many characteristics with the traditional representation of a witch, such as flying on a broomstick and being accompanied by black cats. Her broom also represents her abilities as a good housekeeper, and they say she sweeps the floors of every house before leaving.
The Yule Lads are a group of 13 mischievous pranksters who travel the Icelandic countryside, leaving gifts for children who left their shoes by the window. The gifts are usually sweets of some kind, but children who misbehave traditionally received rotten potatoes.
Olentzero is depicted as a beret-wearing overweight man with a voracious appetite. He works as a charcoal burner. Children carry around effigies of him on Christmas Eve and go from house to house singing Olentzero carols and receiving candy, similar to trick-or-treating on Halloween.
Belsnickel exists in the southwestern parts of Germany, but also in the Pennsylvania Dutch communities of the United States. He is a man covered head to toe in fur clothing who judges whether a child was good or bad during the year. Legend states that he knocks on the door of the house and asks a question or requests a song, and the children would have to oblige him or be whipped. If he was pleased by the response of the children, he would leave candy, but if they reached for it too quickly, they again risked getting whipped.
Tomte is the holiday gift-giver of Sweden and Norway. He is a small gnome varying from only a few inches to just about three feet tall. Originally, Tomte was a sort of house elf who secretly lived in a farmer's house and protected it. Nowadays, believers leave out a bowl of porridge with butter on top for him to eat on his way out.
In Armenia, Christmas is considered to be solely a religious holiday. So Santa (or Gaghant Baba) does not visit until New Year's Eve or sometimes January 6th, which they recognize as the date Jesus was born.
Mikulas is the Hungarian version of St. Nicholas. He is actually not the gift-giver on Christmas Day, but instead leaves candy and nuts in the shoes of good children on December 6th. Mikulas knows that not every child is completely good though, so as a reminder he also leaves a switch behind to remind the children to be good next year. Mikulas is also pretty particular - if your shoes aren't shiny enough, he won't leave anything.