Violence is perhaps the most obvious in the series. Characters are shot, impaled, wounded, etc... In the first episode, we see a Lakota ritual, the Sun Dance. Skewers are placed through a young man's chest and attached to a tether; skewers he eventually pulls through his skin by dancing from sunup to sundown (we see blood and the skin pulled taut). Also in the first episode is a scene in which a group of innocent bystanders are trampled to death by a herd of stampeding buffalo (nothing terribly bloody or graphic here).
One female character is hit by a runaway wagon and subsequently has her leg amputated (we see the gangrenous, maggot-filled wound before the amputation), but the amputation itself is offscreen (an amputation which, we're told, results in the death of the character).
Two characters in one episode fight over gold and both are killed, one by drowning, the other is practically beaten to death. It should be noted that in every episode, there are casualties. Particular episodes of note would probably be: "Hell on Wheels", in which the infamous Washita massacre takes place and we see men, women, and children slaughtered (there is also the Sand Creek Massacre, which takes place prior to Washita). In "Casualties of War" and "Ghost Dance", we see the effects of the Indian boarding schools (children are forced to chew on bars of soap as punishment for speaking their native language, etc.), and in "Ghost Dance", there is a focus on the massacre of Wounded Knee, along with glimpses of the Battle of Little Bighorn.