Continuing the previous posts, here are some of my favorite books for kids 18m - 2yrs. Early toddlers all of the sudden catch a sense of humor. They "get" that something is funny, or sounds funny, or rhymes (or doesn't). Some of the early Seuss board books (not the regular Seuss yet), Doreen Crownan, and Laura Numeroff are all good authors for this age group. For "stories" keep them short (a few words per page) and feel free to condense the story to keep up with your toddler's attention span. Toddlers are increasingly able to learn by example at this age, so keep an eye on what behavior the books are modeling (and whether you are ok with that as a parent). At our house we love some Mo Willems books, but NOT "Don't Let the Pigeon Drive the Bus" because we felt like it didn't show a behavior that we wanted Tot #1 or #2 to mimic. This is purely a personal choice and we may very well be reading too much into what they can pick up from a book, but it is something to think about as you choose books for this age group and beyond.
Some are still board books, but we're starting to dabble in "real" books. The decision of board book vs. hardcover vs. paperback it totally up to you, but be aware, the board book versions of regular books (such as the Dr. Suess books) are condensed versions of the full stories.
Here are some of my favorites: