Very first learning to read books:
Big Brown Bear, by David McPhail
The Flip-A-Word Series, by Harriet Ziefert, ill. Yukiko Kido 
Hop on Pop, by Dr. Seuss
The BOB Books
The Cat and the Cab, by Judy Thoms
Am I A Man? by Judy Thoms 
thoughts on learning to read -- from Deborah
on phonics-based learning to read methods
The Primary Phonics Series (Mac and Tab, etc.), by Barbara Makar
Meet Monster: Six Stories about the World's Friendliest Monster, by Ann Cook and Ellen Blance, ill. Quentin Blake
The Dolch "Pleasure Reading" series, by Edward W. Dolch, Marguerite P. Dolch, and Beulah F. Jackson
the Structural Reading series, by Catherine Stern, Toni S. Gould, and Margaret Stern 
The Yucky Reptile Alphabet Book, by Jerry Pallotas
the Brand New Readers series
Danny and the Dinosaur, by Syd Hoff
Ten Apples Up on Top!, by Dr. Seuss
Disney Peter Pan Level 1 Reader
Next level:
Mrs. Brice's Mice, Sammy the Seal, and others by Syd Hoff
Board books!
The Frances books, by Russell and Lillian Hoban
The Big Blue Book of Beginner Books
Alphabet books:
Kipper's A to Z
The Yucky Reptile Alphabet Book, by Jerry Pallotas
Diaper bag books (good for reading on the subway, planes, etc.):
Jamie  and Angus, by Anne Fine 
Little  Bear, by Else Holmelund Minarik
Little  Bear's Visit
Father  Bear Comes Home
Little  Bear's Friend
the Frog and Toad series, by Arnold Lobel 
Early reader books with multiple  stories in them:
the  Little Bear series, by Else Holmelund Minarik (illustrated by Maurice  Sendak)
No  Fighting, No Biting!, by Else Holmelund Minarik
the Poppleton series, by Cynthia Rylant 
the Frog and Toad series, by Arnold Lobel  
The Golly Sisters Go West, by Betsy Byars 
Mouse Soup, by Arnold Lobel
Friendship:
Elephant and Piggie series, by Mo Willems
Gay-friendly/anti-stereotype:
Pinky and Rex and the Bully, by James Howe
Girly:
Fancy Nancy, by Jane O'Connor
High-interest for reluctant readers:
The Best of Pro Football
National Geographic's Myths Busted
The Cat on the Mat is Flat, by Andy Griffiths
Mystery/Humor:
The High-Rise Private Eyes series, by Cynthia Rylant
Short chapter books:
The High-Rise Private Eyes series, by Cynthia Rylant
Dodsworth in New York, by Tim Egan (also Dodsworth in Paris and Dodsworth in London) 
Junie B. Jones series, by Barbara Park 
The Pinky and Rex series, by James Howe
The Henry and Mudge series, by Cynthia Rylant (and here)
The Boxcar Children series, by Gertrude Chandler Warner
Toon Books:
Silly Lilly in What Will I Be Today? by Agnes Rosensteihl
Little Mouse Gets Dressed, by Jeff Smith
Maya Makes a Mess, by Rutu Modan
Vocabulary-teaching:
the Fancy Nancy series, by Jane O'Connor
 
 
