The idea of aliens abducting us is a relatively new idea. It merges the science fiction and horror genres in a unique way. It is most attributed to the 1940s and 1950s with interesting origins that point directly to the rise of science fiction and space exploration of the time.
It is closely linked with famous UFO sightings of that era such as the Hill Abduction (leading to an Outer Limits episode).
Since those times interest in a good alien abduction movie or story has only grown. It has become a well-known trope used in everything from Pixar shorts to horror movies such as Fire in the Sky and the infamous McPherson tape found footage film.