E. E. 'Doc' Smith was one of the pioneers of "space opera", a sub-genre of science fiction that had grand themes and galaxies as backdrops. Starting with The Skylark of Space, I lapped these up when I was 14 and 15. Along with novels and stories by Jack Williamson and A. E. Van Vogt, these were my first real exposure to American pulp fiction, which led to reading about the old pulps and, in particular, a fantastic set of books called The History of the Science Fiction Magazine by Mike Ashley. In my last year of school, I did a project about British SF magazines which was the first sustained bit of research I ever did. Nearly thirty years later, I'm still finding the whole research thing fascinating.
The 'Doc' Smith books were also amongst of the first sets of Chris Foss artwork I remember seeing, along with his covers on various Isaac Asimov novels. Again, hugely influential on the young me. These really looked like spaceships that could travel from galaxy to galaxy. Wow!
The Lensman Series
The Skylark of Space Series
The Family d'Alembert Series
"The Imperial Stars" originally appeared as a novelette in Worlds of IF (1964) and was subsequently expanded to novel length by Stephen Goldin, who then continued the series, which eventually ran to ten volumes.
Lord Tedric Series
Note: The first novel in the Lord Tedric series was based on a short story ("Tedric") and novelette ("Lord Tedric") which appeared in Other Worlds and Universe in 1953 and 1954 respectively. The stories were woven into a novel by Gordon Eklund and the results published originally as a collaboration in the USA. Eklund then continued the series, although the books remained credited to E. E. 'Doc' Smith.