I just did a similar search online for recommendations, and this is what I found (sorry it's so long). Several are classics, but maybe you can find one or two others that are new to you & your kids:
Whistle for Willie Board Book by Ezra Jack Keats, also Peter's Chair
Caps for Sale Board Book: A Tale of a Peddler, Some Monkeys and Their Monkey Business (Reading Rainbow Books) by Esphyr Slobodkina
Elmer (Elmer Books) by David McKee
Corduroy (40th Anniversary Edition) by Don Freeman
The Happy Lion by Louise Fatio
Happy Birthday, Moon (Moonbear) by Frank Asch
I Stink! by Kate McMullan
The Neighborhood Mother Goose (Ala Notable Children's Books. Younger Readers (Awards)) by Nina Crews
Dear Children Of The Earth by Schim Schimmel
The Incredible Book-Eating Boy by Oliver Jeffers
The Thingamabob by Il Sung Na
Animals Should Definitely Not Wear Clothing by Judi Barrett. 1970.
Are You My Mother? by P.D. Eastman. 1960.
George and Martha by James Marshall. 1972.
Harold and the Purple Crayon by Crockett Johnson. 1955.
Harry the Dirty Dog by Gene Zion. 1956.
The L. Engine That Could by Watty Piper. 1930.
The Napping House by Audrey Wood. 1984.
The Snowy Day by Ezra Jack Keats. 1962.
The Story of Ferdinand by Munro Leaf. 1936.
Bark George by Jules Feiffer. 1999.
Color Zoo by Lois Ehlert. 1989.
Do Pigs Have Stripes? by Melanie Walsh. 1996.
“Hi, Pizza Man!” by Virginia Walter. 1995.
My L. Sister Ate One Hare by Bill Grossman. 1996.
A gross-you-out counting book about a L. sister who will eat anything and everything.
Pig Pig Grows Up by David McPhail. 1980.
A young pig insists on being coddled and treated as a baby, until an emergency forces him to admit he is a “big kid.”
Where’s Your Smile, Crocodile? by Claire Freedman. 2001.
A young crocodile’s bad day turns itself around when he helps a baby lion find his mom.
Food for Thought: The Complete Book of Concepts for Growing Minds by Saxton Freymann. 200
Shapes, colors, numbers, letters, and opposites…oh my!
Lemons Are Not Red by Laura Vaccaro Seeger. 2004.
Are lemons red? Are carrots purple? Children get a thrill out of guessing the true colors of everyday objects.
L. One Step by Simon James. 2003.
Older ducklings teach their L. brother a game so he does not whine about the long walk home.
Squeaky Clean by Simon Puttock. 2002.
Mama Pig has such a hard time putting her three piglets to bed after their bathtime escapades, which cause them great excitement.
Stray Dog by Marc Simont. 2001.
A family is delighted, amazed, and eventually worn out by the stray dog that shows up on their doorstep. A Caldecott Honor Medal winner.
Ten L. Fish by Audrey Wood. 2004.
E WOOD
A counting book with fish so colorful, they seem alive.
Wild About Books by Judy Sierra. 2004.
E SIERRA
How will the animals react when the librarian drives the bookmobile to the zoo?
Fairy Tales and Non-Fiction
Actual Size by Steve Jenkins. 2004.
J 591.41 JENKINS
Animal depicted in their actual size, height, and girth will surprise children and their grown-ups.
Joseph Had a L. Overcoat by Simms Taback. 1999.
E 782.42 TABACK
Joseph creates a smaller piece of clothing each time the fabric becomes “old and worn.”
Seven Blind Mice by Ed Young. 1991.
QE 398.24 YOUNG
Each blind mouse “sees” the elephant as something different from the others in this retold Indian fable.
Sylvia Long’s Mother Goose. 1999.
E 398.8 MOTHER
Classic, memorable nursery rhymes are interspersed with some that are less familiar.
What Do You Do With a Tail Like This? by Steve Jenkins. 2003.
J 573.87 JENKINS
Explores the interesting and surprising ways wild animals use different parts of their body, such as the cricket hearing with ears on its knees. A Caldecott Honor Medal winner.
Building With Dad by Carol Nevius
Cloudy With a Chance of Meatballs by Judi Barrett
Max's Words by Kate Banks
Outside Inn by George Ella Lyon
How I Became a Pirate by Melinda Long
All the World
By Liz Garton Scanlon, illustrated by Marla Frazee
Boo Hoo Bird
by Jeremy Tankard
Bubble Trouble
by Magaret Mahy
Duck! Rabbit!
By Amy Krouse Rosenthal
My Garden
By Kevin Henkes
Wee L. Bunny
By Lauren Thompson; illustrations by John Butler
Wombat Walkabout
By Carol Diggory Shields; illustrations by Sophie Blackall
"More More More," Said the Baby
By Vera B. Williams
The Big Honey Hunt by Stan & Jan Berenstain
This was another huge favourite in our house for many years.
Kids love the story of Small Bear and his 'smart old Dad' who together go looking for honey, only to be faced by one danger after another.
Alfie Gets In First by Shirley Hughes
This gorgeous story is one in a series of stories about Alfie and his mum and dad and baby sister, Annie Rose.
Alfie is about four years old which makes it easy for children of three or four to identify with him and the situations he encounters in the stories.
In this story, Alfie and mum and Annie-Rose return from a shopping trip and, while his mum struggles with the pushchair outside, Alfie rushes inside and slams the door behind him.
So now Alfie's stuck inside and mum and Annie Rose are stuck outside without a key! Soon everyone in the street is trying to help rescue Alfie.
Some of the other stories about Alfie are ...
Alfie Gives A Hand
Alfie's Feet
An Evening at Alfie's
Possum Magic by Mem Fox
Australian children's author Mem Fox has written some wonderful picture books for children.
'Possum Magic', first published in 1983, is the best-known of her books and something of a publishing phenomenon.
'Once upon a time, but not very long ago, deep in the Australian bush, there lived two possums. Their names were Hush and Grandma Poss. Grandma Poss made bush magic ...'
Click here to hear Mem Fox reading Possum Magic.
Diary of A Wombat by Jackie French
At first glance, this looks like a book for much younger children.
Not so!
The humour in this delightful picture book appeals to all ages but especially to three and four-year-olds as they discover just what a wombat' does all day. There are holes to be dug, territory to be defended and lots and lots of eating and sleeping to be done!
Fantastic illustrations and a truly lovely story.
Poems for the Very Young by Michael Rosen
A book of poems and nursery rhymes is one of the best books for young children to own because it's a book you'll read again and again as your child grows.
And children at this age love poetry and rhymes. They're great fun to read and are actually really important from a developmental point of view because they help young children develop phonological awareness, a crucial skill for learning to read.
If you'd like to browse through a list of other collections of poems and rhymes for young children, click here.
A Fish Out Of Water by Helen Palmer
This book is an oldie and the pictures might seem a bit old-fashioned to parents but trust me - kids love it!
This is the story of a boy who buys a fish from a pet shop but fails to follow the instructions given by the man in the pet shop about how much to feed his new pet. The fish grows and grows, outgrowing each container the boy finds to put him in until finally the pet shop man comes to save the day.
One of the best books for young children around.
Whoever You Are by Mem Fox
It's a delight to look at and to read and is also a lovely book to help you teach your child that we are all people first, no matter where in the world we live and that we share more similarities than differences.