A roller coaster was an elevated railway with small passenger cars that operated at high speeds as a ride, especially in an amusement park.
Pacific Park on the Santa Monica Pier on Earth had a roller coaster in 2024. (PIC: "Assimilation")
Roller coasters were still popular in the 24th century. (TNG: "Interface"; VOY: "The Thaw")
In 2370, Geordi La Forge compared the excitement of using the interface suit to being on a roller coaster. (TNG: "Interface")
In 2372, Captain Kathryn Janeway reflected on why children still rode roller coasters after several centuries. The Doctor suggested it was because fear produced pleasure. (VOY: "The Thaw")
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There is a Star Trek: The Next Generation-themed roller coaster in Germany.
The script for the Star Trek: The Next Generation sixth season episode "Aquiel" states "The events of the past few days have taken [La Forge] on an emotional roller coaster", i.e. the events on Relay Station 47. [1]
Similarly, the script for the Star Trek: Deep Space Nine fourth season episode "Body Parts" states that "Kira's on an emotional rollercoaster that she didn't anticipate" when it hits her that she is pregnant. [2]
The script for Star Trek Generations describes James T. Kirk as "a child who has just come off a roller-coaster" after orbital skydiving into a wheat field. [3]
The script for Star Trek: Insurrection states the Son'a collector's sails "almost reminds of the support foe [sic] an old-time roller coaster – a cobweb of crisscrossing pipes, and conduits and planks…" [4]
The script for Star Trek Nemesis describes operating Scorpion-class attack fliers as "like trying to control the world's fastest roller coaster." [5]