(covers information from several alternate timelines)
A cable car was a type of vehicle that operated on a cable railway. These cars were used for transporting passengers and for advertising products. Signal lights governed the movement of the cars. In San Francisco, the cable car system was operated by the San Francisco Municipal Railway and, later, Trans Francisco. One of the lines on this system was Powell & Mason.
Centuries ago, the natives of Beta III used some sort of cable car, or a similar vehicle, as their streets had cable car railways running through them. However, after Landru used his machine to give the natives a hive mind, it seemed that the cable cars were no longer in use, because in the year 2267 there was no sign of cable cars on the streets. (TOS: "The Return of the Archons")
In 1986, as Pavel Chekov and Nyota Uhura were attempting to get directions to the nuclear vessels docked at Alameda from passersby, a cable car filled with passengers was seen making a left turn. (Star Trek IV: The Voyage Home)
By the mid-23rd century, in the alternate reality, the cable cars had been equipped with anti-grav devices. In the aftermath of the USS Vengeance crashing into the city, one of these cars can be seen traveling down a road. (Star Trek Into Darkness)