Meaning that you would read them of your own volition, without a kid to read to. And I mean “picture books” as opposed to “chapter books”.
Here’s my list offhand.
Dr. Suess
The “Frog & Toad” series (& others by this author)
The “Grandpa & Uncle Wainey” series (& others by this author - James Stevenson, IIRC. I believe he is also the author of the “Worst Person in the World” series)
David Wiesner’s very cool and award-winning picture books…Tuesday; June 29, 1999; Sector 7. Extremely imaginative, with beautiful, detailed , funny art.
Allan Say’s work…Tree of Cranes; Grandfather’s Journey; Emma’s Rug; Tea with Milk. Very moving and mysterious stuff, much of it dealing with the author’s inner conflict about being both American and Japanese. Gorgeous artwork also.
(I call it “mysterious” because so much goes on in every book that isn’t explained…who are the American soldiers in The Bicycle Man? Why is the mother so unhappy in Tree of Cranes?)
The Tom Swift Jr. series.
I get a chuckle out of Laura Numeroff’s If You Give A Pig A Pancake.
Another recent goodie is Doreen Cronin’s **Click Clack Moo, Cows That Type.
Zev Steinhardt
The Giving Tree by Shel Silverstein. He also wrote a hilarious parody book entitled Uncle Shelby’s ABZ’s.
I read The Missing Piece by Shel Silverstein purely by accident within weeks of my wife leaving me. Made me cry, but gave me strength at the same time. Amazing what a little advice from a kids book can do.
Click Clack Moo is great and so is the sequel Giggle, Giggle, Quack. Another favorite of mine is The True Story of the Three Little Pigs or just about anything by Jon Scieszka, Lane Smith.
Goodnight Moon has always been my favorite.
Ooh, almost forgot:
Where the Wild Things Are and In the Night Kitchen are also classics that I could read over and over again.
Anything by Roald Dahl.
I like reading the really old Nancy Drews, the first editions, because they’re so quaint.
Laura Ingalls Wilder will always be cool to me.
Susan Copper’s The Dark is Rising series–one of the best fantasy series ever.
Where the Wild Things Are
In the Night Kitchen
Outside Over There
Goodnight, Moon
Tuesday
The Tomten and the Fox
I just re-acquired Paddle to the Sea
If we’re talking picture books:
Ezra Jack Keats!
Chris Van Allsburg
Scieszka & Smith (“The Stinky Cheese Man”)
Dr. Suess
I also like the caldecott books of my childhood & earlier (yes, I realize this makes me an old, crotchety person), some newer ones as well.
I love the “If You Give A …” series by Laura Numeroff. My current favorite, which my son only begrudgingly lets me read to him once every couple of months is No Matther What by Debi Gliori.
THE KING, THE MICE AND THE CHEESE by Eric and Nancy Gurney. It really resonated with me later in life when I found myself trading off little problems for big ones.
Olivia by Ian Falconer. It totally cracks me up.
I’m so glad someone else likes that one.
It was my favourite. 
I also remember being inspired by one called “The Big Ball of String”, but I can’t remember the author.
Dr Seuss influenced me heavily, in my love of the sound of words.
That was my favorite book(s) for years and years! The first book especially is great to read around this time of year. So, another vote for those.
And there are too many others.
Shoshana- I never read Paddle to the Sea, but when I was a little kid the local library showed the film every year. THEN a few years ago, there was a NORTHERN EXPOSURE ep which had a recurring scene of Chris reading it out loud on his radio show.
*Click Clack Moo is one of my FAVORITE BOOKS EVER!
Really.
When I worked in a bookstore, I made it one of my Staff Favorites, and would foist it on anyone who got within a three foot radius of me. If you aren’t familiar with this fabulous book, get to a bookstore now!
I also love Peter Sís’s books, especially Madlenka. Gorgeous, gorgeous illustrations.