(covers information from several alternate timelines)
Asphyxia, asphyxiation, or suffocation was a condition of severely deficient supply of oxygen to the body that arose from abnormal breathing.
In 2154, Enterprise NX-01 discovered that the adult crew of a Xindi-Insectoid ship had suffocated when they transferred power from life support to power the on-board hatchery, protecting their young. (ENT: "Hatchery")
In 2365, Worf bluntly told Danilo Odell that had he been standing under the USS Enterprise-D's fire-suppression system when it was activated, he'd have suffocated and died. (TNG: "Up The Long Ladder")
When Tom Paris operated a 1936 Ford truck in a USS Voyager cargo bay in 2371, the resulting high levels of smoke caused Tuvok to suggest increasing the ventilation before everyone was asphyxiated. (VOY: "The 37's")
Also that year, Jadzia Dax told a miniaturized Miles O'Brien that he'd suffocate if he left USS Rubicon as the oxygen molecules outside were too large for his hemoglobin to assimilate. (DS9: "One Little Ship")
In 2375, Janeway ordered Paris to reroute power from the Delta Flyer's life support systems as added protection from the Borg Queen's vessel, preferring to suffocate than vaporize. (VOY: "Dark Frontier")
When the air was sucked out of Voyager's bridge by a class J nebula lifeform in 2376, Captain Janeway was almost asphyxiated as she attempted to reroute emergency power to environmental controls. (VOY: "The Haunting of Deck Twelve")