One of those parlour games/memes is spreading around. I usually ignore them. But it's seems worthwhile to identify your influences and lazy not to take the time to think it through.
"Influential" turns out to be a trickier concept than it looks like at first. Influences, for one thing, run in both directions, towards and away. Influential doesn't necessarily mean high quality or best or favorite.
Anyway, here's my list of books that changed the way I think about things or that still shape my life.
(Not because I'm Christian, but I grew up in a church where we studied the Word intensively. I read it through, once as a believer and again, later as a heathen.)
War and Peace, Leo Tolstoy
The Sound and the Fury, William Faulkner
The Short Stories of Ernest Hemingway
Zorba the Greek, Nikos Kazantzakis
The Portable Nietzsche, Friedrich Nietzsche, edited by William Kaufman
(Includes the complete Thus Spoke Zarathustra, together with long selections from the Gay Science and Genealogy of Morals as well as letters and essays)
Essays and Aphorisms, Arthur Schopenhauer
Letters from a Stoic, Seneca
Victory, Joseph Conrad
Collected Poems, W.B. Yeats
On Aggression, Konrad Lorenz
Advertisements for Myself, Norman Mailer
Oops, that's 12.
What are your top 10?