An olfactory sense or sense of smell was a sense generally perceived by one's nose though which smells were detected.
Female Vulcans had a heightened sense of smell, but offensive odors, such as the natural odor given off by Humans, could be tolerated by using a nasal numbing agent. (ENT: "Broken Bow", "The Andorian Incident")
In "Ode to Spot", Data noted that Spot's olfactory sense, in addition to his visual and auditory senses, contributed to his hunting skills and natural defenses. (TNG: "Schisms")
Both Data and Lal were programmed with a sense of smell. (TNG: "The Offspring")
The Changeling Odo claimed to not have a sense of smell. (DS9: "If Wishes Were Horses", "Improbable Cause")
When The Doctor was inhabiting Seven of Nine's body, he was not used to having a sense of smell, and so commented negatively on Harry Kim's body odor. (VOY: "Body and Soul")
The Beta Annari possessed 1,253 olfactory receptor genes, which gave them an extraordinarily acute sense of smell; they could detect when another person was lying, what they last ate, and the identity of their last sexual partner. However, their sense of smell could be deceived by someone injected with beta-blockers, anxiolytics, and benzos. (PIC: "Stardust City Rag")