What you should take away from this character profile: Zaphod is the President of the Galaxy who steals the Heart of Gold ship (on his 200th birthday, so it's basically legal, since you can give yourself any present you want on your 200th birthday, right?); he's the semi-cousin of Ford Prefect; he has three arms and two heads; and people love to list his qualities.
We're not kidding about those lists. When we first meet Zaphod, we found that he is an "adventurer, ex-hippy, good timer (crook? quite possibly), manic self-publicist, terrible bad at personal relationships, often thought to be completely out to lunch" (4.11). Trillian notes that he has "dash, bravado, conceit" (11.9).
It doesn't end there. Even the news broadcast has a lot to say about Zaphod. He's "the man who invented the Pan Galactic Gargle Blaster, ex-confidence trickster, once described by Eccentrica Gallumbits as the Best Bang since the Big One, and recently voted the Worst Dressed Sentient Being in the Known Universe for the seventh time" (12.3). As Zaphod himself explains to Ford and Trillian, his brain scan shows that he is "clever, imaginative, irresponsible, untrustworthy, extrovert, nothing you couldn't have guessed" (20.73). All of which raises the question: where can we get a list like that?
One reason why Zaphod seems to be anything and everything is that he's constantly moving and engaging in various schemes. For instance, he's not only the president, but he has a "highly profitable second-hand ballpoint business" (21.8). He's certainly manic, which is why he can be both nervous and excited (11.2). He's the type of guy who can crash a party (that's how he meets Trillian) and break into an Arcturan megafreighter like it's nothing (29.43). He's the life of the party, but he's also the guy who gets you accidentally thrown into jail while he runs off to pursue some other scheme—which will then get added to the list of his accomplishments.
Like his semi-cousin Ford, Zaphod would rather go to a party than save the world from danger—but while Ford is coolly incompetent, Zaphod is the kind of dude who would probably set the party on fire accidentally. One reason for this is that, well, Zaphod just doesn't think too much. We'll have a lot to say about that in a moment.
But the other thing is that our friend Zaphod is very interested in style—and in making a great big scene. Big fire = big scene. As the narrator notes, "Zaphod loved effect: it was what he was best at" (4.27). That's why he makes such a great president of the galaxy: since the role of the president is merely to seem important and powerful and let other people really have the power and importance (4.14). That's right, folks: our Zaphod is a drama queen.
Look at the scene when Zaphod steals the Heart of Gold, for one thing. He spends most of the time thinking about what the scene of this theft will look like to the other people there—or at home watching on Tri-D: "Zaphod smiled, picturing himself" (4.35); "He grinned at them [the press] particularly because he knew that in a few moments he would be giving them one hell of a quote" (4.48). As Trillian succinctly notes, he's a huge "show-off" (4.53).
So we can diagnose Zaphod: he's obsessed with style and being the center of attention. (It's like they made one of the show hosts on the E! network into the president.) So when he thinks Trillian has picked up some hitchhikers, he's not happy, but he gives her "ten out of ten for style" (11.8).
However, like most drama queens we know, Zaphod is also hugely insecure and quite nervous. We don't feel bad saying this about him because he says it himself: "I'm very insecure" (12.10). When he gets voted "Worst Dressed" (12.4), we can bet it's because, in an attempt to get attention, he's gone too far into just plain ridiculous territory. Sure, he might look like a suave guy, but even when we first meet him, it's hard not to notice that he's a ball of nerves: "Zaphod Beeblebrox paced nervously up and down the cabin, brushing his hands over pieces of gleaming equipment and giggling with excitement" (11.2). This is Zaphod Beeblebrox in a nutshell: he's nervous and excited at the same time.
Actually, that's not so difficult for a dude like Zaphod. After all, he has two heads.
Zaphod's second head is kind of a mystery in the book. We know he only had one head when he visited Earth and picked up Trillian (13.65). It would almost make more sense if each head had a different personality, but they don't (unless you watch the movie version—about which we shall not deign to speak). For instance, when Trillian's mice escape, his heads react the same way: "An expression of deep worry and concern failed to cross either of Zaphod's faces" (19.8). He just… has two heads.
(As for the TV version, we'll be honest: the joke about having two heads works great on the radio… but not so well on TV, especially if you've got a small budget.)
But that's a great segue, if we do say so ourselves, into the fun issue of Zaphod's brain issues. Did we mention that Zaphod has sealed away part of his brain? What does that mean, you ask? Well, one thing it means is that, like most people, Zaphod sometimes doesn't know why he does stuff. Zaphod is a pretty mysterious dude even to himself: "And then whenever I stop and think—why did I want to do something?—how did I work out how to do it?—I get a very strong desire just to stop thinking about it" (20.71).
Unlike the rest of us, however, this seems to be working out pretty well for Zaphod. This comes up several times: "Trillian had come to suspect that the main reason why he had had such a wild and successful life that he never really understood the significance of anything he did" (11.9); and Ford thinks that Zaphod " never appeared to have a reason for anything he did at all: he had turned unfathomability into an art form" (14.5). Well, that's one way to turn something that sounds bad into something good. Zaphod doesn't understand stuff, and he doesn't explain stuff to his friends, but he has turned this into "an art form," and his life is actually pretty successful.
But let's take a step back: why do you think Adams describes Zaphod in this way, and why do we get this description of him so often? One good reason is that if Zaphod knew everything and could tell us about it, then this adventure would probably be a lot easier for the characters and a lot less funny for us. Here's a thought experiment: take one of the Hangover films, put in James Bond, and what do you get? Instead of some incompetent fools running around making us laugh, you'd have a super-competent guy solving the problem really easily. So by giving Zaphod this mental problem, Adams keeps the story funny.
There's probably a thematic reason here, too. That is, Zaphod can be pretty foolish at times, but he can also be pretty smart. And, honestly, who hasn't felt like that at one time or another? Zaphod may be this crazy, famous president, but he's got something that all of us can relate to: he can occasionally be an idiot.
Oh, yeah. There's also that bit about him being the president. Wait, you say, a political figure with two heads who doesn't know why he does what he does and is mostly interested in being famous and making people notice him, thereby causing all kinds of problems for everyone around him? Right. We've never heard of that sort of thing before, either.
Zaphod's main role in the book is to cause problems, though sometimes it must be said that his problems solve other problems. For instance, Zaphod steals the Heart of Gold, which causes the cops to come after him—but those cops show up just in time to help everyone escape from Magrathea. Arthur's job is to give us someone to identify with; Ford's role is to guide Arthur through the problems; Zaphod's role is to cause problems by doing things that he doesn't understand.