There are, in my estimation, three main audiences for works of psychology: curious members of the public with a humanistic desire to know about their fellow creatures, those attempting to self-medicate and those with a professional interest. Each will get something out of Rollo May's work on anxiety but likely also experience some dissatisfaction.
The curious: they will likely be the most disappointed. They might enjoy the individual case studies of `Harold Brown' and the women pregnant out of wedlock. Even though they are short, there is a richness to them. They might also find inspiration in May's conclusions about how anxiety is not something entirely awful but is in many ways central to the human experience, particularly as we attempt to grow, for May argues that normal anxiety is part and product of risk and development.
On the other hand, the nicest thing that can be said about May's prose is that it is very `workman-like'. May obviously was a very smart fellow and in certain ways, this book isn't as dated as it should be for being thirty years past its second edition. But there is something dry about his prose. There is no panache, no elegant turns of phrases. Indeed, even though you can tell May is enthusiastic about his topic, he isn't able to get you to feel it.
The self-medicating bookworms: I suspect that they will only find interesting the initial discussion, up to Kierkegaard, in which May lays out his ideas, and then the ending, in which he tries to draw conclusions from his case studies. There's a whole lot of book between those, so if I were looking for help, I'd just read the beginning and ending at a library and call it a day. (But note that at least one reviewer motivated by their own pain has a better assessment on this score than myself.)
The professionally inclined: my sense is that the person who would get the most out of this book is a grad student in psychology who is on summer break the year before they do their orals. The first half of the book is an overview of anxiety from a number of different angles, attempting to define anxiety (as opposed to fear) and explain its causes. May doesn't pretend to be exhaustively cover each view, but he does give a good sense of different perspectives and this is two-hundred pages of lit review that would be worth the shelf space and money to actually buy, though his historical approach to anxiety seems a little breezy. (It's worth noting that in the biology chapter in particular has a strong proto-cognitive behavioral streak.)
The synthesis and clinic investigation that make up the second half of the book probably won't do much for a professional. May considers himself a post-Freudian, but he's probably not post-Freudian enough for modern audiences. He'll do things like interpret a response to a Rorschach ink blot as an erupting volcano as symbolizing a woman's upcoming labor and birth. And his relating anxiety almost entirely to childhood rejection seems a little pat, even if his arguments are intriguing. (That's the one part of the book that borders on provocative.)
So a curious, anxious psychologist might enjoy the whole book. Everyone else, I suspect, will get a lot out of some parts but get impatient in others.