An ion-powered starship from Sigma Draconis VI
Ion propulsion was a highly-advanced propulsion system used on both ground vehicles and starships.
The use of ion propulsion for allowing ships to travel faster-than-light was considered by Starfleet to be only theoretical as of 2268.
In that year, the starship USS Enterprise encountered a vessel from Sigma Draconis VI which utilized ion propulsion. The crew eventually discovered that the technology had been developed in the distant past, and that its users could only operate it for short periods of time while under the influence of the Teacher. (TOS: "Spock's Brain")
Some Akritirian starships used ion-based propulsion, fueled by paralithium. (VOY: "The Chute")
In 2383, the Runaway; a land-based vehicle on the USS Protostar ran on ion propulsion. (PRO: "Dream Catcher")
According to the Star Trek: Starship Spotter, the Jem'Hadar attack ships featured ion propulsion units as warp nacelles. The attack ships could achieve a maximum speed of warp 9.6.