OK, here's my 15, in no particular order. Ask me tomorrow and I'll probably give you a different list.

The Hitch Hiker's Guide To The Galaxy - Douglas Adams
Slaughterhouse-5 - Kurt Vonnegut
The Puffin Joke Book (1974) - Edited by Bronnie Cunningham (lot of very surreal, twisted and dark humour for a kids' joke book, which I bought aged 8 and still dip into occasionally)
Macbeth (OK, not a book strictly speaking, but I have loved it ever since I first read it) - Shakespeare
Portnoy's Complaint - Philip Roth
1984 - George Orwell
Brave New World - Aldous Huxley
Notes From A Small Island - Bill Bryson
This Other Eden - Ben Elton
The Dynamite Kid - Brian Blessed
History Without The Boring Bits - Ian Crofton
Tough Boris - Mem Fox
Is That It? - Bob Geldof
Any children's book by Robert Munsch
Memoirs Of A Geezer: Music, Life, Mayhem - Jah Wobble

Catch 22 - Joseph Heller
Something Happened - Joseph Heller
A Brief History of Time - Stephen Hawking
The Blind Watchmaker - Richard Dawkins
The Naked Ape -Desmond Morris
Mila 18 - Leon Uris
1984 - George Orwell
The Lord of the Rings/The Hobbit - Tolkien
The Iliad/The Odyssey - Homer
The Fountainhead - Ayn Rand
Carnage and Culture - Victor Davis Hanson
Presumed Innocent - Scott Turrow
North Dallas Forty - Peter Gent
The Bible - God
QB VII - Leon Uris

EDIT: I just have to add this one. One of the most devastating books I have ever read. Non-Fiction. A survivor and escapee from Auschwitz. I read it when I was in high school and it was out of print and very difficult to find until 10 or 15 years ago. For those who deny this history, read this book, but of course, you won't.

I Cannot Forgive - Rudolph Vbra

The Lord of the Rings
Mr. Lincoln's Army
One flew over the Cuckoo's Nest
The canterbury tales
Of Mice and Men
Frankenstein
On the Road
Howl
1984
The number of the Beast- Heinlein
The Time Machine
The War of the Worlds
The Monkey Wrench Gang
The Prince
Meditations- Aurelius

Gone with the Wind - Margaret Mitchell
Gorky Park - Martin Cruz Smith
Painted Faces - LH Cosway
Lolita - Vladimir Nabokov
A Density of Souls - Christopher Rice
Half Asleep in Frog Pajamas - Tom Robbins
Still Life with Woodpecker - Tom Robbins
Birds of Prey - Wilbur Smith
Swan Song - Robert McCammon
Lord of the Flies - William Golding
Wayward Pines - Blake Crouch
Bag of Bones - Stephen King
How to be a Domestic Goddess - Nigella Lawson
Aztec - Gary Jennings
Interview with the Vampire - Anne Rice

Mine are far less scholarly, but these books stuck with me because of how I felt when I read them and what they left me with when I was done... and I tend to read at the level of a high schooler apparently, ha!

1984
Alice in Wonderland
The Chocolate War
A Clockwork Orange
The Count of Monte Cristo
Fahrenheit 451
Flowers for Algernon
The Giver
Harry Potter (series)
The Handmaid’s Tale
Lord of the Flies
The Outsiders
Ready Player One
The Shining
The Stand

Not necessarily my all-time favorites, but they’ve influenced me in a variety of ways. ???

The Hitchhiker's Guide to the Galaxy - Douglas Adams
Dune - Frank Herbert
Adolf Hitler: My Part in his Downfall - Spike Milligan
Foucault's Pendulum - Umberto Eco
Trainspotting - Irvine Welsh
He Died With a Felafel in his Hand - John Birmingham
Pretty much everything written by Terry Pratchett, but Mort is an old favourite
Only Forward - Michael Marshall Smith
The Diamond Age - Neal Stephenson
Vurt - Jeff Noon
Pattern Recognition - William Gibson
The Crow Road - Iain Banks
Excession - Iain M. Banks
Fear and Loathing in Las Vegas - Hunter S. Thompson
The World Book Encyclopedia

Histories; Herodotus
Lolita; Nabokov
Mila 18; Uris
No jail for Thought; Kopolev
Cancer Ward; Solznyitsin
Hanto Yo; Ruth Beebe Hill
Don Quixote; Cervantes
Selection of short stories; Maupassant
Tales from a Hunters Album; Turgenev
My name is Asher Lev; Polok
The Peleponnesian War; Thucydides
The Chronicles of Thomas Covenant; Donaldson
The campaigns of Alexander; Arrian
The Threepenny Novel; Brecht

I read books for fun, not for influence, but I did read some classic books when I was FAR too young and they negatively influenced me..like the original Gulliver's Travels, which made me cynical about humans.

I have read hundreds, if not thousands, of books that have genuinely influenced me and my life. But, at age 81 I don't try to remember the titles.All that I can say is that any person who has not done substantial serious reading has profoundly limited his or her intellectual and moral development.

The Selfish Gene by Richard Dawkins
A Brief History of Time by Stephen Hawkins
Animal Farm by George Orwell
Eating Animals by Johathan Safran Foer
The Catcher in the Rye by J. D. Salinger
Brave New World by Aldous Huxley
Atlas Shrugged by Ayn Rand
Catch 22 by Joseph Heller
How Not To Die by Dr. Michael Greger, MD
A Short History of Nearly Everything by Bill Bryson
Moonwalking with Einstein by Joshua Foer
Food, Inc. -- Karl Weber, Editor
Freakonomics by Steven D. Levitt & Stephen J. Dubner
The Republic by Plato
1984 by George Orwell
Stranger in a Strange Land by Robert A. Heinlein

Some great read, no doubt. but... heavily male-influenced.

Here are 15, not in any particular order:

"Never at Rest: A Biography of Isaac Newton", Richard Westfall
"Economics In One Lesson", Henry Hazlitt
"Operational Amplifiers, Design and Applications", Jerald Graeme
"Adventures of Huckleberry Finn", Mark Twain
"Atlas Shrugged", Ayn Rand
"Ninety-Three", Victor Hugo
"John Adams and the Spirit of Liberty", C. Bradley Thompson
"Writing and Thinking", Norman Foerster, J. M. Steadman
"Logic, an Introduction", Lionel Ruby
"How to Raise a Brighter Child", Joan Beck
"Introduction to Objectivist Epistemology", Ayn Rand
"The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design", Richard Dawkins
"Equal is Unfair: America's Misguided Fight Against Income Inequality", Don Watkins, Yaron Brook
"The Psychology of Self-Esteem", Nathaniel Branden
"John D. Rockefeller, The Heroic Age of American Enterprise - Volumes I & II", Allan Nevins

Bobby Henderson - The Gospel of the Flying Spaghetti Monster!
God is Not Great - Christopher Hitchens

Sword of Truth Series: Terry Goodkind
Shannara Series: Terry Brooks
Sense & Goodness without God & On the Historicity of Jesus: Richard Carrier
Still Foolin' 'Em: Billy Crystal
Kiss me like a Stranger: Gene Wilder
God is Not Great: Christopher Hitchens