When Wyatt, Virgil, and Morgan Earp are preparing to confront the Cowboys at the O.K. Corral, Wyatt tells Doc Holliday "It's not your problem. You don't have to mix up in this." to which a visably hurt Doc replies "That is a hell of a thing for you to say to me" and takes up his place next to the brothers.
In its own way, Doc's explanation for why he sticks with Wyatt:
Doc Holiday: Wyatt Earp is my friend.
Turkey Creek Jack Johnson: Hell, I got lots of friends.
Doc Holiday: (long pause) I don't.
Minor one but at one point Doc coughs in Wyatt's drink to prevent him from getting drunk. The fact that he knows Wyatt wouldn't risk getting TB just to get drunk shows that he is willing to help his friend in the most depressing situations.