I see a lot of great titles listed here already. As I put together this list, I noticed most of these "life changer" books entered my life in my late teens/early 20s.
Breakfast of Champions - Kurt Vonnegut
Most Vonnegut books played a fairly prominent role in my life, none as important as this one though. I've probably re-read it 15 times. I remember my dad noticed I was reading it when I was 16 and he looked bewildered, like he was in a time warp, and told me he also read that book around my age. I once met a person with a tattoo of a quote from this book and I looked at him and said, "is that Vonnegut?" and he looked at me like I was the only person in the world that understood him. Love love love this book. Won't ever get rid of my tattered copy from Half Priced Books that I obtained as a teenager.
The Fountainhead - Ayn Rand
Another life changer, probably because I read it when I was 19 or so. I'm not a huge Ayn Rand fan now as an adult, but this book will always hold a special place for me, especially when I crack it open and see what content 19-year-old-me underlined... I was a total destroyer of books at that age but I enjoy having insight into my mind at that age.
Siddhartha - Herman Hesse
Another one I re-read multiple times, well into my early 20s. It just really struck me at the time. It feels fuzzy in my mind now, having forgotten most of the story. I want to read it again now...
Walden - Henry David Thoreau; Self Reliance - Ralph Waldo Emerson
I smooshed these together because I was reading both of these around the same time and they may be to blame for some of my crazy, f-off into the desert to build an Earthship dreams.
Watership Down - Richard Adams
God I read some heavy shit as a young person... another favorite though, and I watched the movie adaptation many times as well.
You Get So Alone at Times That it Just Makes Sense - Charles Bukowski
I distinctly remember picking up this book based on the title alone, and I loved it and went on to read a lot of poems from Bukowski. Bukowski was a poet and a self-proclaimed dirty old man, but dang, at that age (early 20s), he GETS ME.
Slanky - Mike Doughty
Soul Coughing was by far my favorite band growing up, so there was no question that I was going to dive into this book of poems by Doughty. I made sure I obtained an original copy of this book at a concert in my 20s and only regret now that I am no longer really enjoying his new music as an adult.
Gunslinger Series - Stephen King
And because apparently I allowed myself to read some "fun" books too, I would throw the Gunslinger series on the list, just because I could get lost for days in these books. I've re-read these books many times, despite how lengthy they are. I see they are coming out with a movie this year as well so I'm excited to see how they might approach it.