No Name Given: "Ford Prefect" is an alias used on Earth due to Ford believing that cars were the dominant life form on the planet. His real name was only pronounceable in an obscure and extinct Betelgeusian tongue, and Ford's inability to pronounce it caused his father to die of shame. His schoolmates called him 'Ix', which meant "boy who is unable to satisfactorily explain what a Hrung is, or why it should collapse on Betelgeuse Seven", the cause of his original language's extinction.
Multiple Head Case: Subverted in most adaptations (where there's no distinction between the two heads), pretty much played straight in the movie, and zigzagged in the sixth novel, where the second head has a distinct personality after being removed and attached to the Heart of Gold.
Screwy Squirrel: He is a complete scoundrel, will almost screw anything over for personal gain, and FAR from a role model. Practically the reason why he is the president of the galaxy in the first place, actually.
That Man Is Dead: In the backstory he lobotomised himself to keep his plans secret even from himself. However, turns out that the 'new him' hates the old one and actively works against those plans.
Catch Phrase: "I think you ought to know I'm feeling very depressed", "Life? Don't talk to me about life." some of the first two lines he says when introduced in every continuity of H2H2. Thgere's also his "Here I am, brain the size of a planet..." speeches.
The Chew Toy: He literally gets treated like crap (or makes himself believe he is, at times) by almost everything in the entire universe. The fact that he is several times older than the universe itself in the later books doesn't help much, either.
Flawed Prototype: Marvin was the unsuccessful prototype for the emotion chip. Everything else that has it is irrepressibly cheerful all the time-- including Eddie, a ship AI who will cheerfully tell you you're about to be vaporized by nuclear missiles, and even the individual doors which all thank you for passing through them. Marvin hates them all.
Image Song: He had four such songs sung by Stephen Moore, his actor from the original radio and TV series.
Ridiculously Human Robot: Subverted. While humanoid, his emotion chip is supposed to emulate real emotions. Unfortunately, it does that too well, and only with depression.
Robot Buddy: Under certain definitions of the word "buddy". The marketing division of the Sirius Cybernetics Corporation was probably referring to a different robot when it advertised "Your Plastic Pal Who's Fun To Be With!"
Talking the Monster to Death: In one instance, Marvin defeats a sentient armoured tank by asking it to guess what weapon he has been given with which to defend Zaphod against it. When he reveals that the answer is "Nothing", the tank gets so angry that it blasts out the floor, causing it to plummet to its destruction.
In the first book, he kills two policemen on Magrathea by plugging up to the ship controlling their life support system and having a long chat, explaining to it his opinion and perspectives of the Universe...
Ford: And what happened?
Marvin: It commited suicide.
A lot later, amongst the swamps of Sqornshellous Zeta, he recalled to the matress Zem the time he, some miles away and five million years earlier, had opened a bridge meant to revitalize the economy of the Sqornshellous System (after the entire economy of the Sqornshellous System had been spent building the bridge) with a depressing speech in which he expressed his spiteful contempt for everyone who would ever cross the bridge in question and then plugged into the bridge's opening circuits.
Zem: Voon, and was it a magnificent occasion?
Marvin: Reasonably magnificent. The entire thousand-mile-long bridge spontaneously folded up its glittering spans and sank weeping into the mire, taking everybody with it.
Time Abyss: Oh so very, very much. In one instance he stays in one spot from approximately 1980 untill the end of the universe. By the end of the series he is, by virtue of Time Travel, six times older than the universe itself! ...He is then brought back to life again because numerous characters that lived when he was created were still alive, and that went against the Lifetime Insurance Policy of Sirius Cybernetics Corporation.
"The first ten million years were the worst. And the second ten million, they were the worst, too. The third ten million I didn't enjoy at all. After that, I went into a bit of a decline."
Noodle Implements: How Wowbagger became immortal involves a rubber band, a boxed lunch, and a high-powered particle accelerator. People who have attempted to recreate the circumstances that made him immortal have failed, looking very stupid (or very dead) in the process. Or both.