Unconsciousness
If the person is unconscious with no obvious sign of life, you might need an ambulance. If you or any bystander has the necessary skills, why not give them mouth-to-mouth resuscitation while you wait.
Bleeding
If the bleeding is bad, you might want to stop it by applying firm pressure to the wound (use something clean you fools) and raise it above the level of the heart. Lay the person down, reassure them, keep them warm and loosen tight clothing.
Burns
For all burns, cool with water for at least 10 minutes. Wrap the affected part in clingfilm, do not apply dry dressings, keep the patient warm and call an ambulance. If the casualty is a zombie, let the bastard burn.
Broken bones
Try to avoid broken bones, they hurt.