"Random" was a word that was popular to use for about a decade or so, in the late 1990s and early 2000s. Beyond being an oft-used and abused word, it was an entire aesthetic, where incongruous things were matched up with each other. Often these "random" things were not as "random" as they seemed to be, being drawn from a rather limited lexicon of wackyness. See, for example, Mr. T ate my balls. The aesthetic of "Random" was a major force in the early development of the world wide web, with many examples from this site's early years.

I believe that "random" as a slang term has probably receded, although given the psychology and sociology of late adolescence, the underlying idea probably has not. But perhaps randomness can not be seen as that great of a thing where so many ukulele covers of 80s pop songs exist on youtube, and where no less of an arbiter of culture as xkcd has declared it obsolete.