(covers information from several alternate timelines)
The Golden Gate Bridge was a suspension bridge in San Francisco, California, built in the 1930s. It spanned the Golden Gate, the border between the San Francisco Bay to the east and the Pacific Ocean to the west. The bridge was one of the most iconic symbols of San Francisco.
During their visit to 1986 San Francisco, Admiral James T. Kirk and Spock rode a bus over the bridge. Upon their return from that year, their captured Klingon bird of prey HMS Bounty nearly crashed into the bridge. (Star Trek IV: The Voyage Home)
The bridge was heavily damaged during a Breen attack on Earth in 2375, during the Dominion War. However, within a year the damage to the bridge, and the city, had been repaired. (DS9: "The Changing Face of Evil"; VOY: "Pathfinder")
The bridge was also imperiled in the alternate reality's 2258 when the Narada fired its drilling beam at Earth next to the bridge, right over the inlet of San Francisco Bay. When the rig's tether was destroyed and the drilling platform fell, it barely missed hitting the bridge. (Star Trek)
The Golden Gate Bridge has only once been mentioned in dialog by name, in "Past Tense, Part I", but is seen in virtually every establishing shot of San Francisco. Coincidentally, the one time it was mentioned by name was one of the times it was not seen in an establishing shot of the city.
The only time that Star Trek actors have visited the real Golden Gate Bridge for production purposes was during Star Trek IV: The Voyage Home when William Shatner and Leonard Nimoy rode across the bridge on a bus. The words "Golden Gate" are also spoken during the film, but in reference to Golden Gate Park.