It isn't easy being a cop!
~ One Galactic Policeman

The Galactic Police are recurring antagonists in the series The Hitchhiker's Guide to the Galaxy and are after their old President, Zaphod Beeblebrox.

The Hitchhiker's Gude to the Galaxy

The old President is in a coma, and his successor, Zaphod, only became President to steal the Heart of Gold ship. The Galactic Police became angered and sent down men to kill Zaphod and anyone with him. They corner Zaphod, Arthur, Ford, Tricia and Marvin on planet Magrathea, and are going to kill him when the policemen suddenly rant about how awful their own lives are. Suddenly, Marvin sends his "depression virus" out to the ship's main computer, causing it to commit suicide, and then the men's life-support battlesuits die and they suffocate to death.

The Restaurant at the End of the Universe

Tricia comments that maybe someone at the Milliways restaurant tipped off the Police when they saw Zaphod arrive, and then Zaphod comments that maybe they want to arrest him over the phone, which he thinks would be a very odd move.

Also, an old friend of Zaphod's, Hotblack, is spending a year "dead" for tax reasons, meaning he is on the run from the Police.

So Long, and Thanks for all the Fish

Ford Prefect is on a rundown planet and is in the HanDold city where a police battle is going on, between a rogue band of musicians, and the police are shooting at the skyscraper where the band is killing bass players. The Police here seem to be more comedic relief, although Ford does have to evade them several times in the story, such as when he knocks one policeman out, freezes him in his ship, and puts it round the Pleiades star system as punishment, hoping to bankrupt the Police.

Mostly Harmless

By this time, the Police had been corrupted with the Vogons and now seek to destroy anyone who is opposed to InfiniDim Enterprises.