Berlinghoff Rasmussen was a 22nd century inventor from New Jersey on Earth. During this period, he stole a 26th century time-pod from its rightful user and used it to travel forward in time. His plan was to collect future technology for dismantling and study in hopes of recreating it in his own time and taking credit.
In 2368, Rasmussen visited the USS Enterprise-D claiming to be a professor of history from the future. Despite his putting on a cheery and eccentric demeanor, the crew had a hard time believing this initially and tried to avoid asking questions regarding the future. Eventually, however, Captain Picard asked for Rasmussen's help in what action he should take regarding a planet the Enterprise-D was trying to save. Rasmussen covered his lie by claiming saving the planet may allow the existence of another Adolf Hitler or Khan Noonien Singh.
During this time, Rasmussen stole various objects to smuggle back to his time, including a phaser. He became enamored with Doctor Beverly Crusher, a feeling she did not return. He also attempted to abduct Data, but the phaser he tried to use had been deactivated. The Enterprise-D senior staff confronted him about the thefts, and Picard ordered Worf to arrest Rasmussen despite his pleas to be let go. The pod vanished, stranding him in the future. Worf led Rasmussen to the brig, with Picard welcoming him to the 24th century and remarking there were "more than a few legitimate historians at Starfleet who will be quite eager to meet a human from your era." The Enterprise subsequently deposited Rasmussen at Starbase 214. (TNG: "A Matter of Time")
In 2372, as part of an effort to prove Worf's claim that the Enterprise-D, unlike Deep Space 9, was immune to security breaches, was false, Odo cited the case of Rasmussen, among others. (DS9: "Bar Association")
Background information Edit
Rasmussen was played by actor Matt Frewer.
The script for "A Matter of Time" described Rasmussen as "a kindly-looking Human male in his late forties [...] wearing a drab, nondescript jump suit and a baggy 'lab' jacket."  According to the script for "Bar Association", his name was pronounced as "BERR-ling-hoff ras-MYU-sen". 
The Star Trek: The Next Generation Companion spells his first name as "Berlingoff".
Rasmussen appeared in the Pocket DS9 novel The Big Game, in which he was released from prison in 2369. He then traveled to Deep Space 9, where he participated in a high stakes poker tournament held at Quark's. The novel also mentioned that Rasmussen claimed to have been on Titanias III during the early 2150s, where he met a Klingon who identified himself as being a member of the House of Duras.
In the Star Trek: Strange New Worlds short story Research, Berlinghoff had the foresight to hide blueprints for the time-travel pod prior to his journey, and was able to retrieve them and successfully rebuild it. He then traveled back to the late-20th century, to the home of his ancestor, J. R. Rasmussen. Together, they travel back to 1964, where they relay information about the future to a television writer named Gene Roddenberry. Rasmussen died sometime before 1999 in an auto accident, while driving to an appointment with producers at Paramount Pictures.
Berlinghoff Rasmussen also appeared in the novel Indistinguishable from Magic.