I also believe that writers should read as much as they write. I suspect any writer who can't say who their influences are--they either have not read much, or widely, or they love one writer or school of writing and are just copying their style.
Another good rule is: Good in, good out. Read good stuff...Life is too short to spend much time reading junk.
That all having been said, there are a couple of books all writers should read/use. Hopefully you can find these at your favorite bookstore but I've included Amazon links, if not.
These are some of my favorites:
The Artist's Way
My friend (and inspiration) Judy Reeves' A Writers Book of Days
The Little Red Writing Book
On Writing
The Elements of Style
And the book that started it all for me, in terms of reading about writing, Natalie Goldberg's Writing Down the Bones
I also love Bird by Bird
A newcomer to this distinguished group of books on writing is The Accidents of Style: Good Advice on How Not to Write Badly
Tonight is the much-anticipated launch party/reading/event for John O'Melveny Woods swashbuckling pirate yarn, Return to Treasure Island
Happy reading...and writing...
Hasta pronto!