(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.
In 1986, the location of this bridge was depicted on a San Francisco Municipal Railway map. Later that year, while visiting San Francisco after traveling from the 23rd century with a group of Starfleet officers, Admiral James T. Kirk and Spock rode a bus over the bridge. Upon the group's return from 1986, a Klingon Bird-of-Prey they had captured, HMS Bounty, nearly crashed into the bridge. (Star Trek IV: The Voyage Home)
In 2258, after receiving a distress call from Vulcan, shuttles ferrying Academy cadets to the starships docked at Starbase 1 flew over this bridge. Later, while preparing to demolish Earth, the Romulan mining vessel Narada fired its drilling beam 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)
In the alternate reality of 2259, Golden Gate Bridge was seen in a map of the San Francisco Bay. This map was part of a collection of graphics and video media that were displayed on a powerwall in the offices of Admirals Christopher Pike and Alexander Marcus at Starfleet Headquarters. (Star Trek Into Darkness)
The bridge was heavily damaged during a Breen attack on Earth in 2375, during the Dominion War. However, within a year, the damage to both the bridge and the city had been repaired. (DS9: "The Changing Face of Evil"; VOY: "Pathfinder")
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 ruins of the Golden Gate Bridge were at one early point to be shown in 23rd century San Francisco, as opposed to the intact bridge, in Star Trek: The Motion Picture. For that film's director's edition DVD release, real footage of the Golden Gate Bridge was incorporated by Foundation Imaging. (Star Trek: The Magazine Volume 2, Issue 8, pp. 97 & 53)
The only time that Star Trek actors have visited the real Golden Gate Bridge for production purposes was during the making of 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.
When planning the crash of the USS Enterprise-D's saucer section for Star Trek Generations, the Golden Gate Bridge, measuring 1.2 miles long, was used as a scale reference for the saucer section. (The Art of Star Trek, p. 290)
Upon conceptualizing San Francisco from the 2250s of the alternate reality for the film Star Trek, the Golden Gate Bridge was featured in several different versions of how the city might look. The bridge was imagined as existing merely as a monument, since it was conceived that people used hovercars rather than continuing to require bridges. However, one concept image – an illustration of the Narada's laser drill firing into the San Francisco Bay, clearly incorporating a contemporary photo of the bridge – showed the structure supporting fossil-fueled automobiles. (The Art of Star Trek, pp. 50-51 & 150-151) The Golden Gate Bridge, as shown in the Star Trek movie, contained no futuristic-looking CGI adornments, unlike much of the rest of San Francisco. The bridge was integrated into plates intact, projected onto two-dimensional cards. Shots that the bridge was inserted into include footage set in the grounds of Starfleet Academy, with the bridge added to the background. Aerial plates taken above the bridge were used by Industrial Light & Magic when they were generating shots of the Narada's massive drill falling into the San Francisco Bay. (Cinefex, No. 118, pp. 60 & 70)
Similar to how they had imagined the Golden Gate Bridge in the film Star Trek, the filmmakers of Star Trek Into Darkness decided, while designing San Francisco for that film, that nothing had much changed about the bridge since contemporary times, even following the Narada's attack in the previous film. (Cinefex, No. 134, p. 72)