Ole-Luk-Oie is the Danish version of the Sandman, most famously described by Hans Christian Anderson in a story by the same name. His name is in two parts: Ole is a common Danish name, and Luk-Oie means "eye-shutter." He carries two umbrellas. One is covered with wonderful pictures inside, and this he holds over good children and gives them good dreams. The other is black, and this he holds over bad children, who then have no dreams and sleep heavily, and wake unrefreshed. He has a brother, also called Ole-Luk-Oie, whose other name is Death; he also shuts peoples' eyes.
The first three pictures here are from illustrations of Anderson's story; the fourth is from the Soyuzmultfilm feature The Snow Queen, where Ole-Luk-Oie (played by Mickey Rooney in the English dub) is narrator; and the fifth is from a proposed Disney feature that never got made. The story has influenced both James Branch Cabell (with Miramom Lluagor, the Lord of Dreams, and his half-brother Death) and Neil Gaiman (with Morpheus the Sandman and his sister Death).
For a really grotesque vision of the Sandman, look up E. T. A. Hoffman's version.