I believe they are missing several he published under "Gill Hunt" or "Keith Woodcott [Brunner]".
Brunner's work varies drastically in quality and tone. There are often discussions as to "how many" Brunners there are, some people pointing to at least three. I think the way you have to reconcile this is to see him as a thorough pro, who often wrote entertaining stuff that would sell on very tight schedule. However, he also experimented with several other types of work, and some of the experiments had remarkable results. He more or less admitted this himself in an interview, saying that he actually put his full effort into only a handful of his books.
Brunner is probably best known as some sort of "King of the Dystopian", and we should probably start here. I did. I thought of him as a specialist who wrote incredible Dystopians, until I picked up a few of his other works.
I'm not including "Shockwave Rider" with this group, which many people would. OTOH, many people aren't familiar with "The Jagged Orbit", which is a shame.
Brunner's dystopians are masterpieces of that subgenre - most of the people who dislike Brunner point to TSLU and SoZ and complain about them being so totally depressing. Whether they are or not, Brunner did his homework for these books, researching, and extrapolating a worst case scenario for some particular issue: ecological disaster in "The Sheep Look Up", overpopulation in "Stand on Zanzibar" and urban violence / racial tensions in "The Jagged Orbit".
The result is often a future that seems all too likely if we don't watch it, followed mercilessly out to nihilist conclusions. It's aided by Brunner's writing style for these novels - lots of quick cuts, exposition through excerpted news broadcasts and advertising, snippets of future popular culture. He supposedly borrows his style from John Dos Passos' "USA" trilogy, which I haven't read, but I definitely mean to. Brunner is very good at coming up with plausible future slang and popular culture, and uses them here to etch his extrapolated nightmares on the brain.
David Brin mentioned TSLU in his forward to "Earth", discussing the difficulties of writing a 50 year ahead projection, as opposed to a shorter or longer range novel. I think TSLU stands as a better work even not considering the intervening years - IMO, Brin missed with that one. Not that many people seem to be aware of "Jagged Orbit". It's as good as the other Brunner dystopians. I reread JO at the time of the Rodney King episode, and there was that impression again - that Brunner was unsettlingly prescient.
Highly reccomended.
This book establishes that Brunner is actually the founder of cyberpunk, whatever you may have though about that Gibson guy. Like the dystopians, it is the result of Brunner doing his research. What he was extrapolating in this case was "information overload", and he was obviously influenced by Alvin Toffler's book "Future Shock", which was in vogue then. I don't include this work with the dystopians partially because it has a an upbeat ending, one might even say uplifting. This is the "serious" Brunner for the people who find TSLU and SoZ "depressing".
Brunner creates a future heavily computer networked society which isn't to bad, technically, even by modern standards, and was downright amazing considering 1975 as a vantage point. The protaganist is a uber-hacker. See - cyberpunk.
Highly reccomended.
Quite possibly the best SF novel with no human characters. It covers many generations of an alien civilization progressing from primitivism to a scientific society. Similar to Robert Forward's "Dragon's Egg" in that way. Not nearly as strange a setting, but interesting enough, and Brunner was a far better writer than Forward will ever likely be. Brunner's aliens are alien enough not to be "humans in funny suits", but the characters are still accessible to the reader, and he does his exposition of their odd physiogamy and its features without intruding. Nice trick, that.
Highly reccomended.
More political thriller than SF. The story concerns an urban planner in a future untramodern city in a South American state, and his entanglement in its corrupt politics. Well written, one of the "non-pulp" books, but it possibly should be reviewed by fans of John Grisham or Robert Ludlum rather than myself.
Try it. You might like it.
Five short fantasy stories concerning journeys made by an enigmatic and shadowy "traveler" imposing law on the chaos he encounters through the mechanism of granting wishes, usually with very instructive results which were not what the wishee intended. I think of this as Brunner trying to be Roger Zelazny - it's a game try, but Zelazny's better at it.
Highly thought of by many people, not particularly liked by me.
We enter the realm of the less "serious" Brunner here. I think this may be the best of his "entertaining" writing. It is set in a future where Earth has interstellar flight, a couple colonies, and peaceful commerce with several alien races, and many of humanities problems seem to have been solved. The protaganist is a young diplomat who must deal with a crisis involving an apparent xenophobic conspiracy emanating from one of the colony worlds, which is also attempting to overtake the home world in influence. Straightforward, well-crafted story.
Reccomended.
Also titled "The Telepathist".
The protaganist has remarkable telepathic powers, and a terribly deformed body which cannot be repaired. Rescued from a menial existence and escape into mental fantasy worlds (a danger for the telepathic), "The Whole Man" is a story of his maturation and development. Much more of an individual character study than Brunner usually did, and the character is easy to empathize with.
Highly Reccomended.
An archeology team explores the remains of a long dead, highly advanced civilization on Sigma Draconis, attempting to determine what caused it to collapse, perhaps allowing Earth to avoid a similar disaster. Another well-crafted, straight forward story, perhaps rather dated for the modern reader, but quite enjoyable if you can correct for that.
Reccomended.
A creature from the sea takes over the body of a downed pilot and staggers ashore, disrupting a rock concert on its way to terrorizing a seacoast town. Too conciously "60's", and as much of a b movie plot as it sounds like.
Give it a pass.
Revised and republished as "Catch a Falling Star", 1968
Set in a post-technological-collapse society one hundred thousand years in the future, they deal with the impending near collision with a star.
OK, I think. I remember rather liking it, but cannot remember that much about it.
In a grim and screwed up future Europe, a small group of British citizens discovers a viral drug which might enforce utopia by making the religious zealots and war mongers rational and peaceful - do they have the moral right to use it.
I can't remember much about this one, either.
Revised and republished as "Age of Miracles, 1973
Alien invaders novel, in which the aliens essentially trash mankind's civilizations offhandedly.
Pretty pedestrian - skip it.
A town is enveloped in a mysterious fog which causes everybody to act in unorthodox ways. Soon, the town is the focus of hordes of seekers of mystical experiences, while the protaganist tries to figure out wht is really going on.
Give it a pass.
A well crafted story of the surprises a planet has in store for a group of colonists. Another of the straight forward enjoyable Brunners.
Pretty good.
Brunner doing a comedy - a time machine has been invented, which the scion of a rich family is going to use to have a "reunion" with his illustrious ancestors. Unfortunately, it allows the young twit to find out what they were REALLY like.
Amusing in spots, but pretty forced, too. Brunner doesn't really have the touch for out and out comedy.
Done late in his career. Sort of a travelogue of a ship revisiting planets that had been seeded by human colonization so long ago they are becoming alien.
Basically boring. Skip it.
In a decaying near future, a science writer is trying to unravel the mystery of a group of children that can seemingly get away with major crimes. The secret may be mankind's salvation. This had potential, but Brunner telegraphed his punches so badly that the reader will have the whole story figured out half way through the book.
Not reccomended.
Awful. Horrible. Don't go anywhere near them.