The Tangut script. The Tangut script was a logographic writing system used by the Tangut people of the Western Xia dynasty (1038-1227) to write their language, the now-extinct language of Tangut, of the Tibeto-Burman branch of the Sino-Tibetan languages. The language and script together are attested between 1036 and 1502.
The Tangut script is notable for its great complexity - its characters typically consist of far more strokes than their Chinese counterparts. No Tangut character is directly based on any Chinese character; the overall concept of the writing system and the forms of individual strokes were all that were borrowed. The characters include no phonetic or pictographic elements or references whatsoever; their forms are completely arbitrary and abstract.
The [Tangut] language is remarkable for being written in one of the most inconvenient of all scripts, a collection of nearly 5,800 characters of the same kind as Chinese characters but rather more complicated; very few are made up of as few as four strokes and most are made up of a good many more, in some cases nearly twenty. It is extremely difficult to remember them, since there are few recognizable indications of sound and meaning in the constituent parts of a character, and in some cases characters which differ from one another only in minor details of shape or by one or two strokes have completely different sounds and meanings. - Gerard Clauson
I think the Tangut script is one of the most aesthetically pleasing writing systems that I have read about; for me, its great cumbersomeness only enhances its beauty. This script is also a great reminder for conlangers that developing a logographic script does not necessarily require going through any kind of pictographic stage at all.