I read a TON of board books to both of my kids when they were little. There are still a few that we keep around here just for sentimental reasons, even though they are both teenagers now.
One of my daughter's favorites when she was a baby was a version of Edward Lear's poem The Owl and the Pussycat with illustrations by Jan Brett. I must have read this to her a thousand times, it seems.
Another classic that both of my kids enjoyed was Goodnight Moon by Margaret Wise Brown. I think everyone has probably heard this story about the little rabbit who wants to go to sleep:
One more great board book is The Snowy Day by Ezra Jack Keats. This is about a little boy named Peter who explores the city on a very snow day: