Literally anything that you can die from in Oregon Trail. Take your pick: Drowning, starvation, thirst, horrible diseases, rattlesnake bites, crushed by a falling wagon... Dysentery seems to be the most infamous because of the internet meme. If you don't know what dysentery actually is, google it. It's not a pleasant way to go. At all.
Oh, you can also randomly get eaten by bears and cougars during the hunting mini game. That's right. Red Dead Redemption may have made getting cougar'd infamous but Oregon Trail invented it.