There were some constraints placed on the list that affected the books selected. Davies was trying for a diverse mix of subgenres and themes, so in some ways diversity overrode influence in making the selections. He also limited the list to no more than one book from each author, so highly influential authors are woefully underrepresented. (How can you choose only one book to represent the canon of authors such as Heinlein, Asimov, Clarke, or Bradbury?)
Working within the constraints as defined, in some cases, I would have chosen a different book to represent some of these authors.
Stranger in a Strange Land for sheer influence, rather than Starship Troopers. However, my favorite Heinlein book has always been The Door Into Summer, which has been a favorite of mine since about fourth grade.
The White Mountains, over Davies' selection of The Death of Grass or No Blade of Grass. The White Mountains has been very influential in introducing generations of new young fans to the science fiction genre. Read my review of The White Mountains.
Rendezvous with Rama quite a bit, but I agree with commenters who said that Childhood's End would have been a better selection to represent Arthur C. Clarke.
Additions to the List
There are some books and authors that I was surprised to find weren't represented on the list. A list that excludes Andre Norton, E.E. Doc Smith, and A.E. van Vogt can't really be considered representative of the greatest works of science fiction.
Andre Norton is probably best known for her Witch World fantasy series, but she was also well known for her adventure science fiction for young adults. Storm Over Warlock was significant as an early science fiction adventure novel with a female protagonist.
E.E. "Doc" Smith's Lensman series is probably the foundation on which all other space opera is based. Although some of the societal aspects of the story are pretty cringeworthy by todays standards (ie., racist and sexist) it's still a shining example of what space opera could be. As a teen I loved the sweeping story that traveled through time, space, and history. Although Triplanetary is listed as the first book in the series, I believe that First Lensman was originally the first book and Triplanetary was added later as a prequel (similar to what John Christopher did with When the Tripods Came).
Slan is another book that was a big influence on my younger self. It's been a long time since I read it, but from what I remember of it, it would have a lot of appeal for today's fans of dystopian literature.
Some of the modern selections seem odd to me. Although I respect that it's sometimes difficult to identify which of the newer books will have lasting value, I disagree with more of his modern selections than the classic ones. I've never been able to get more than a few chapters into a China Miélville book; I just don't enjoy them and don't see the appeal. And while I loved Cory Doctorow's Little Brother, it's very much a product of its time, and I'm not sure it will have the lasting value to be included on a list like this.
What are your thoughts, fellow SFF fans? What science fiction (not fantasy) would you include on a list of essential science fiction books?