Final answer:
Endotracheal intubation is the type of airway adjunct that can be used in conscious, semiconscious, or unconscious patients with or without a gag reflex.
Step-by-step explanation:
The type of airway adjunct that can be used in patients that are conscious, semiconscious, or unconscious, and present with or without a gag reflex is endotracheal intubation. This procedure involves placing a tube into the trachea to maintain an open airway to the lungs and seal it off from the oropharynx. It is commonly used during general anesthesia to ensure proper ventilation and oxygenation.