Everything a person has read influences and inspires what they write. Writing really is a community affair in that respect. Fantasy has been heavily influenced by Tolkein and what he laid forward, and so on. People take in what they read and it becomes accepted into their 'internal canon.'
So: what are some book series that heavily influenced me or inspired me? What is my 'canon?' Although I don't passionately read fantasy or science fiction, the answer is going to be a variety of mostly fantasy.
The first few series that come to mind are:
Russell Kirkpatrick's The Broken Man/Husk Trilogy: This is a very 'unknown' series of books, and I feel unjustly so. I have only read through it once, but I have listed it here because from time to time I think about the ideas the author presented in them. The characters find the true nature of the gods, defeat the gods, use metaphysics as a weapon, immortality is discussed as a negative, and there was even a detailed map of the entire world. The world building aspect really stuck with me. Kirkpatrick created a rich world with interesting characters and I just ate it up. I recommend anyone who reads to try to read them.
George R. R. Martin's A Song of Ice and Fire aka the Game of Thrones series: GRRM has really taken over the fantasy genre in some aspects. He is like a monster that has consumed the attention of fans. He has a TV show for his books and people obsessively analyzing every detail (I am referencing the /r/asoiaf subreddit of Reddit; it is a fantastic and sometimes hilarious place.) The books themselves, taken from the popularity, are pretty amazing. There is a ton of detail and planning, dozens upon dozens of characters, and a robust world. Seeing how much effort he has put into his writing inspired me to do the same. Basically he made my perfectionism worse.
J.K Rowling's Harry Potter: I just felt that I couldn't leave them out. They are what really got me interested in reading. There are problems I have with the series, but there are many things that I love about the books. I think what they did more than anything else was to help me figure out what I wanted to do.
One day I might list off a few non-fantasy options, but those are the three major ones I can recall.