The Hitchhiker's Guide to the Galaxy trilogy (all 5 books) are absolutely the books with the greatest impact on my life ever.
I got the first book as a christmas gift when I was 13 (over 30 years ago). I started reading it that evening at my grand-parents' house. I only put it down to sleep that night. Then, I finished it the next day. And as soon as I was done, I started over.
I got Restaurant at the End of the Universe from a friend (borrowed, then he gave me the book) and read that in about 2 days. Then read Life, the Universe, and Everything shortly thereafter. I think I read all three of those books through at least a dozen times over the next couple months.
I got So Long and Thanks for All the Fish when it came out and read through that immediately. Of course, I then had to re-read the first 3 books and read the 4th again after that.
I somehow hadn't heard about Mostly Harmless until my friend showed up at my house with a hardback copy of it signed by Douglas Adams (and stamped with a 42).
Adams' sense of humour has shaped a lot of my own and his views on the world we live in and life in general have served as a very strong navigation point for me throughout my adult life.