When my niece turned 1, I got her a ton of books... board books, sensory books, squishy books made out of fabric, anything I could find that was appropriate for 1 year olds! Mostly, I got them at Barnes & Noble; they had a great selection then (though now she's 4! eek!)
THis one is NEAT!: Barnes*&*Noble.com - Books: Monday the Bullfrog, by Matthew Van Fleet, Book and Toy, book & plush toy
some books listed as 'baby's first book': Barnes*&*Noble.com - Children's Books: My First Book & Games
Board books - Barnes*&*Noble.com Books - Board Book (Eric Carle books are very popular!)