When writing time is scarce, I sometimes even berate myself for reading instead of writing. As if reading is procrastinating. In fact, reading is the best way to recharge. Why?
The first reason most people already know: reading great writers builds vocabulary and reveals technique. I read other people's fiction and notice things like plotting, voice, or suspense. Francine Prose in Reading Like a Writer reminds me to go deeper: "All the elements of good writing depend on the writer's skill in choosing one word instead of another." Slow down, she commands, and I do.
The second reason is well-noted by other writers. When we take ourselves away from our work -- to exercise, to run errands, to read -- the puzzles that stump us suddenly get solved. New stimuli turn things around and an answer comes.
The final nice reason to read other stuff is for research. I'm always surprised by how much learning something new gives me a fresh approach to a plot or character problem. All of these things help: talking with friends, observing people, reading nonfiction (and not a writing craft one!). So read! Newspapers, blogs, books, magazines!
I've come to feel that you just can't be a writer in a vacuum. (George Saunders just said the same thing much more eloquently in a New York Times interview.) So, the next time you moan about not enough time, don't resent your obligations too much. The work we do among the congregation of humanity is as necessary as solitude. Reading -- like conversation -- is just another way we encounter the material we need.