When Zaphod Beeblebrox is first introduced, he is the runaway President of the Galaxy, a figurehead position with no actual power. He has also visited Earth and taken Trillian away from Arthur, the protagonist. His motivation through the first book is simply the pursuit of money, fame, and self-gratification; he is bored with his life and wants an idealized life of adventure and glory. However, since he is relatively undereducated, impetuous, and easily distracted, he is more likely to get himself and his friends into danger than adventure:
Whatever Zaphod's qualities of mind might include -- dash, bravado, conceit -- he was mechanically inept... Trillian had come to suspect that the main reason he had had such a wild and successful life was that he never really understood the significance of anything he did.
(Adams, The Hitchhiker's Guide to the Galaxy, Google Books)
As the series continues, Zaphod becomes paranoid that his actions are being controlled by some other force; he cannot identify it, but he is aware that his extreme hyperactivity and distractibility are not normal. Finally, he discovers that he himself altered his own brain so as to forget some vital piece of information, and that becomes his driving force: Zaphod wants to find out who is influencing him, why he went along with it, and how to stop it if possible. While his character remains mostly the same throughout, he shows a better understanding of mortality and empathy towards others as the series continues.