Owl Babies
Chicka Chicka Boom Boom
My Monster Mama Loves Me So
And my son’s favorite, “The Little House”. (An oldie but goodie.)
I also vote to not get the classics everyone thinks of like Goodnight Moon. She is likely in one way or another to get those and there is also so much new material.
That said, every library should have a little Curious George. 
Boys and girls!
Some culturally diverse books: https://www.nbcnews.com/know-your-value/feature/8-awesome-children-s-books-celebrate-diversity-ncna974726
Mary Wears What She Wants is getting a lot of excellent acclaim.
I love giving board books at a baby shower. The teacher in me likes educational books. I like “Chicka Chicka Boom Boom”. (Oops, didn’t see it was already mentioned in post 20)
I would also consider the interests of the parents. For instance a friend’s daughter was expecting. The two of us are both Blackhawks fans and I learned her daughter and husband are too. I included “Hockey Opposites” and “Hockey Shapes” with my gift and the personal touch was appreciated.
Also NOT Very Hungry Caterpillar (another one very likely to get another way) but other Eric Carle titles. I really like The Secret Birthday Message. https://www.amazon.com/Secret-Birthday-Message-Eric-Carle/dp/0064430995
Oh! Another one that kids love! The Book WIth No Pictures by Ryan Novak. An instant classic and a must read aloud book. This is the perfect book to give a soon to be dad.
I loved McPhail books like this one:
Also James Stevenson has fun illustrations and slightly wacky tales for the preschool set.
From the Dr Sues thread, Mr Brown Can Moo Can You
Sandra Boynton’s anything. Roald Dahl’s revolting rhymes for anyone with a sense of humor.
Another vote for The Voyage to the Bunny Planet. We have a small set of the trio that are some of the most charming books ever.
I also like to give Boynton’s boarf books Barnyard Dance (which we did dance to with our babies!) and The Going To Bed Book.
Everywhere Babies by Susan Meyers (illustrations by Marla Frazee) is one of my go-to baby gifts.
The Monster at the End of This Book by Jon Stone.
For recent books, look at this list of the best board books of 2018, by a great children’s librarian:
http://blogs.slj.com/afuse8production/2018/12/01/31-days-31-lists-2018-great-board-books-pop-up-books/
I give babies the same gift at every shower…my two kids’ favorite children’s books.
- Harold and the Purple Crayon. It was my son’s all time favorite.
- Blueberries for Sal. It’s written by Robert McClosky who also wrote Make Way for Ducklings. Blueberries for Sal was my DDs favorite book.
- When appropriate...we give a copy with nice illustrations of The Night Before Christmas. In our family, we didn’t use an advent or any other countdown calendar leading up to Christmas. We read 24 holiday books. The one on December 24 was the Night Before Christmas. I would put the books on a bookshelf and read them one by one...and when the only one left was this book, the kids knew it was Christmas the next day.
The Richard Scary- I am a bunny book (I may have saved that one in a box of son’s stuff- found it two or three years ago at Target for a nephew’s son when we visited them). I love it.
Haven’t read all the responses, but my fav (and my kids loved it too) was Goodnight Mr. Night. When my kids received it, it came with a stuffed “Mr. Night” but I don’t think that’s around anymore.
I love baby books! Here are some we had, and some we still have:
Baby Beluga
Pat The Bunny
Brown Bear, Brown Bear
Paddington Bear
Winnie The Pooh
Tales of Beatrix Potter (series)
Guess How Much I Love You
Dear Zoo
Owl Babies
on The Night You Were Born
A child can never have too many books! I think your idea is wonderful!
Good Night, Gorilla!, by Peggy Rathmann, is one of our grandson’s favorites. I read it at least ten times last week. He also loves the books by Caroline Jayne Church - Good Night, I Love You, Ten Tiny Toes, and I Love You Through and Through. His First 100 Words by Roger Priddy is almost worn out.
Just adding…I have been to a number of baby showers where folks were asked to bring a book instead of a card. In a couple of cases, someone bought a small bookshelf for the baby too…and the books were placed in it at the shower.
For the last 10+ years I like to give this combo to new moms: Llama Llama Red Pajama by Anna Dewdney plus some red pjs. I don’t think books for newborns necessarily have to be “board” books. It can also be perfect timing to jump start their new library. This book my preschoolers (now 21 & 18) loved! I pair it with red pjs that are usually size 9 to 12 months (on purpose) - so they have something “new” to wear many months after all the newborn clothing gifts have been outgrown.
Our family still has regular discussions about our 9 favorite kinds of pie, and also why porcupine might have been considered deserving from Harold & the Purple Crayon. 
Any and all Taro Gomi board books. Both my kids absolute favorites! Bus Stops and Spring is Here were two of their number ones, but we had many more and they were beloved.
Don’t Let the Pigeon Drive the Bus by Mo Willems.
Click Clack Moo (can’t remember the author)
The Snowy Day (Ezra Jack Keats)
Guess How Much I Love You
The True Story of the Three Little Pigs
The Runaway Bunny