The makers of some of the later Star Trek series liked making references to this film. The fact that a good chunk of the art department from Next Generation on through Enterprise previously worked on Buckaroo Banzai may have something to do with this.
In one episode of Angel, Yoyodyne is mentioned as a client of evil law firm Wolfram & Hart.
The Wire: In the fourth season episode "Know Your Place", Prez goes to a teachers meeting where standardized test scores get discussed, and it reminds him of his days as a police detective, where it was all about the stats rather than doing any meaningful work. One of the other teachers replies, "Wherever you go, there you are."
The Canadian Synth-Pop artist Glass Apple Bonzai includes references to the film throughout his work, if the cover art on the first two albums wasn't a dead giveaway where much of the inspiration comes from.