1. Last and First Men by Olaf Stabledon
2. Flatland by A. Abbott
3. World of Null-A by A.E. van Vogt
4. Voyage to Arcturus by David Lindsany
5. Everlasting Man by G.K. Chesterton
You might raise an eyebrow at this list, since it contains four sf books and one work of Christian apologetics, but, let me justify:
In terms of sheer scope and inventiveness, Stabledon is still unmatched, even by more modern writers: a universe and all eternity was too small to contain his imagination.
Flatland is a short and sweet meditation on the fourth dimension, and a fable on the folly of intellectual certainty.
Null-A was a seminal book for me, not in the least because it was the first of the 'paranoid thriller' type, later reworked by Philip K Dick, where the hero is not sure who he is. Beneath its pop-psychology gimmick, the book actually touches on some profound ideas about the nature of reality and identity.
Arcturus is a 'paranoid thriller' set in an unearthly spiritual universe, the giant planet Tormance, where two deceptive gods try to cheat the Prometheus of that world out of the divine fire he is carrying back to mankind. A strange, strange book, but one which has more new ideas, and wilder, than any other I've read. I have puzzled over what two new primary colors might look like, or a third positive sex, or five new sense impressions.
I almost chose Chesterton's 'Man Who Was Thursday' as another 'paranoid thriller', this one set in a Christian mythology, against a background of a secret policeman's struggle against the Supreme Anarchist Council. But it is a little predictable, and the end reminds me too much of that English humor for oddness we see in Avengers or The Prisoner.
I am picking 'Everlasting Man' because it is like one of these amnesia thrillers written by Van Vogt, except that here it is autobiographical, and the main character, Chesterton himself, sets out to arrive at the most heroic and wild and rebellious philosophy he can, and then finds himself in the posture of the most conservative of Western thought, the Catholic Church, and he lets out a gust of immense, world-shattering laughter. For those of you who mistrust or even hate Christianity, reading this book might show you the romance, as wild as anything on Arcturus, of what seems a trite religion. I list it here not necessarily because I agreed with Chesterton when I read it, but because this book was also the first place I came across anyone who doubted the commonplace assumptions of modernity.