It is said that he was never photographed (which, of course, adds to his considerable mystique). So we have to go by drawings. Here are two that I have found; apparently regarded as the best ones.
The sketch above was done by William J. Bordeaux around 1952, based (as Wikipedia states) "on a description of him by both Bordeaux's father, Louis Bordeaux, and Crazy Horse's relative, Julia Clown (aka Iron Cedar Woman). Both Bordeaux and Clown said he was never photographed, and they knew him personally."
The portrait below appeared in the article by the Oglala Lakota Charles E. Trimble, "What Did Crazy Horse Look Like?," Indian Country Today, 28 July 2005. The text below it is his own:
Descriptions of Crazy Horse's facial and physical features are abundant, both from Lakotas and a few whites who knew him well. These are included in letters, transcripts of interviews and in books based on those primary sources, and all are consistent in their descriptions. These descriptions generally help disprove the claims of authors and some respected historians that any photo purported to be that of the great leader is the real thing.I found seven more recent portraits online (one / two / three / four / five / six / seven).
Sometime prior to 1940, Oglala Lakota artist Andrew Standing Soldier rendered an ink and watercolor sketch based on descriptions of old men and women who knew Crazy Horse personally. Standing Soldier created extremely accurate portrayals of Lakota life in the 1930s and 1940s, as well as of historic events. Of his Crazy Horse portrait, relatives and close friends of the war leader reportedly pronounced it an excellent likeness.