Africa Counts: Number and Pattern in African Cultures by Claudia Zaslavsky is a unique resource for understanding other cultures and math development. Adult text, readable, activities suggested. Not specifically for multiplication, but activities facilitate understanding of cultural approaches to multiplication.

Alice in Pastaland: A Math Adventure – Cute picture book, take off on the famous story but with math based storyline

Amanda Bean's Amazing Dream (Brainy Day Books) ► Cindy Neuschwander/Marilyn Burns - Wonderful intro to idea of multiplication as fast counting

Anno's Magic Seeds  ► Anno, Masaichiro & Mitsumasa – Advanced for addition / subtraction, but see article for ideas how to use with younger ages

Arctic Fives Arrive  Pinczes, Elinor J - Skip counting by fives

Arithme-Tickle: An Even Number of Odd Riddle-Rhymes ► J. Patrick Lewis

Bats on Parade by Appelt, Kathi – Multiplication concepts demonstrated through arrays of bats through 10x10

Bean Thirteen by Matthew McElligot – Division intro. Two bugs gather 13 beans and try to devise a way to share them evenly. In the end they still have "bean thirteen" left over. Fun book.

Best Ever Math Sticker Book - Usborne, as far as sticker books go, this one stands out

Building Tables on Tables: A Book about Multiplication (Young Math) by John V. Trivett – not a story line, but a very good introduction to multiplication

Bunches and Bunches of Bunnies Louise Mathews, introduction to multiplication

Cheetah Math: Learning About Division from Baby Cheetahs by Ann Whitehead Nagda

Digging for Dinosaurs (Math Adventures) - multi concept reader introducing the math used in real life professions

Division (Question of Math) by Cato, Sheila; Sweeten, Sami

Each Orange Had 8 Slices Paul Giganti, Jr - Counting book with skip counting and grouping ideas

Elsie Times Eight Natalie Babbitt, fun story about a girl multiplied by 8 by a inept fairy

Googol Power: Multiplication Vacation DVD - My kids didn't care that much for the addition / subtraction CD, but the DVD was highly enjoyed and has some math history references in the storyline

Greg Tang Books  - Ages are suggested by publisher. The younger books are written with addition strategies in mind, but are a stepping stone to skip counting and multiplication. The latter books are specifically for multiplication. 
Math Fables (ages 3-6) ► combining numbers for addition
Math Fables Too(ages 4-8) follow up to Math Fables
Grapes Of Math (Mind-Stretching Math Riddles)(ages 7-12) - advanced addition, moving into multiplication); 
Math Appeal (ages 7-12) another book on advanced addition strategies
Math For All Seasons ►(ages 5-8) combining numbers for addition
Math-terpieces, The Art of Problem-Solving (ages 5-12) ► - math puzzles around famous art works
The Best of Times (ages 7-12)
Math Potatoes: Mind-stretching Brain Food (ages 8-13)

Greg Tang Books: The Best Of Times, I did not like this one as much as his others, but it has value - the multiplication is too complex too quickly for intro level, Amanda Bean is better for introducing multiplication; Grapes Of Math  (advanced addition, moving into multiplication); Math Appeal (Mind-Stretching Math Riddles) - grouping and skip counting; Math Potatoes: Mind-stretching Brain Food

The Greatest Guessing Game: A Book About Dividing (Young Math) by Robert Froman – unusual book introducing division

Hello Math Readers:  Just Add Fun! (Hello Reader Math) by Joanne Rocklin - Multiplication. L. 4 / One Hungry Cat (Hello Math Reader. Level 3) ► Joanne Rocklin - Division, hilarious illustrations, this is a family favorite / 98, 99, 100! Ready or Not, Here I Come! (Level 2) Skip-counting to 100 by 2s, 5s, 10s and 20's. / 512 Ants On Sullivan Street (Level 4) by Losi, L. – Doubling

Henry and the Boy Who Thought Numbers Were Fleas ► by Marjorie Kaplan

Lion's Share – A Tale of Halving Cake and Eating It, Too by Matthew McElligott ► – fun book to introduce ideas of fractions and repeated halving, a quick favorite here

Marmaduke Multiply's Merry Method of Making Minor Mathematicians – small format book of timeless multiplication rhymes

Marvelous Multiplication: Games and Activities that Make Math Easy and Fun by Lynette Long

MathStart by Stuart Murphy:  Leaping Lizards (MathStart 1) (Counting by 5s and 10s L.1); Divide and Ride (MathStart 3) Nice book about a group of 11 kids dividing up to enjoy amusement park rides; Double the Ducks (MathStart 1) Doubling numbers; Spunky Monkeys on Parade (MathStart 2) Counting by 2s, 3s and 4s; Too Many Kangaroo Things to Do!: Multiplying (Mathstart: Level 3) Multiplication intro

Minnie's Diner: A Multiplying Menu ► by Dayle Ann Dodds, very fun story about doubling with a surprise ending

Multi-Concept Resources: See list below.

Multiplying Menace: The Revenge Of Rumpelstiltskin (A Math Adventure) ► – unique story involving multiplying by fractions as well as whole numbers

My Full Moon is Square ► Pinczes, Elinor J. - Introduction to square numbers

Now for My Next Number!: Songs for Multiplying Fun by Margaret Park 0915556383

One Grain Of Rice: A Mathematical Folktale ►► by Demi, similar to the King's Chessboard, but set in India, exponential doubling, outstanding illustrations w/foldout pages for the largest numbers

One Hundred Hungry Ants by Elinor J. Pinczes - Division, factors, very clever early intro

One Hundred Is a Family by Pat Munoz Ryan - Combinations that make 10, counting up by 10s to make 100.

One Hundred Ways To Get To 100 by Pallotta, Jerry

A Remainder of One► Pinczes, Elinor J. Division, factors, clever early intro

Riddle-Iculous Math ► by Joan Holub, fun book, riddles, puns, etc.

Sea Squares ► Y Hulme, Joy - Beautiful intro to squaring with marine animals, not busy, could appeal to older kids with artwork

Senefer: A Young Genius in Old Egypt (Young Readers) ► by Beatrice Lumpkin - wonderful living book on several accounts, but as Senefer learns the Egyptian way of writing numbers, it emphasizes how number bases are constructed. Addition and multiplication are woven in the story as well.

Socrates and the Three Pigs by Mitsumasa Anno - How many ways can three little pigs be placed in five houses so that no two are in the same house? Advanced concepts, but can use for mult & skip counting

Spaghetti and Meatballs for All!: A Mathematical Story ► Marilyn Burns - Wonderful intro to ideas of division

Stacks of Trouble by Martha Brenner. Multiplication

512 Ants On Sullivan Street (Level 4) by Carol A. Losi - doubling exponentially

The Doorbell Rang Big Book ► Hutchins, Pat 1986 Multiplication/division/Fun w/cookies

The Essential Arithmetricks – A Murderous Maths book by Kjartan Poskitt

The Adventures of Penrose the Mathematical Catand Further Adventures of Penrose the Mathematical Cat by Theoni Pappas ► – numerous math concepts explored in each chapter

The Great Divide: A Mathematical Marathon Dayle Ann Dodds, nice book on halving

The King's Chessboard  ► Birch, David/Grebu 1988 Doubling exponentially (therefore intro to base 2). Based on historical tale

The King's Commissioners (A Marilyn Burns Brainy Day Book) ► by Aileen Friedman, tallies and grouping to facilitate counting, multiplication

The Multiplication Tables: Colouring Book : Solve the Puzzle Pictures While Learning Your Tables - If you like this one, there's a second coloring book available

The Number Devil: A Mathematical Adventure ► Enzensberger, Hans Magnus/Berner, Rotraut Susanne 1997 Multi-concepts, cute illustrations. Fun classic, very wide appeal, can be read aloud to even very young kids

The Phantom Tollbooth Norton Juster ► – a classic chapter book with math and language ideas woven in, fantasy

Two Hundred Rabbits Lonzo Anderson

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

You Can, Toucan, Math by David A. Adler, Word Problem Solving

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Multi-Concept Resources: These resources cover many math concepts, including skip counting, multiplication and division:

Cyberchase ► PBS show, hugely popular and valuable 30 minutes - ages 4 to 10 ish? Some fun but heavy duty math!

Fractals, Googols, and Other Mathematical Tales Pappas, Theoni Many math concepts, lots with topology, logic and problem solving, wide age range appeal

Galaxy Getaway (Math for Martians) ► by Ferris, Julie; Tassie, Jane – This is a multi-concept book that uses a story-line to present a series of puzzles using a variety of math skills

I Hate Mathematics! (Brown Paper School Books) ► Burns, Marilyn/Weston, Martha General math/math history. Classic

I Love Math Series, Timelife ► - There are 13 of these multi-concept books, each with themes ranging from sports and nature to space and the mall. They are out of print, but still available. See the "I Love Math" page for the list of books with brief descriptions. These may be the most read math readers in our home library over the past decade.

Math for Smarty Pants, a Brown Paper School book ► by Marilyn Burns – this one is for approximately 4rd grade on up. TONS of different math ideas in this.

Math Smart Junior: Grade School Math Made Easy  (Princeton Smart Juniors Grades 6 to 8) ► Lerner, Marcia Princeton Review, 1995 dumb name but great story math book for upper elem, my son read this repeatedly, for older kids (concepts start at addition and move to early algebra)

Math Smart Junior II: More Math Made Easy (Princeton Review Series) by Paul Foglino (for upper elem / middle school) – topics not covered in Math Smart I including history, words and numbers, metric system, number bases

Math Wizardry for Kids by Margaret Kenda and Phyllis S. Williams- activities, stories, games

Mr. Base Ten Invents Mathematics by Bethany H. Tucker. Very simple story-based math.

Planet Omicron (Math for Martians) ► by Ferris, Julie; Tassie, Jane – Math puzzles along with a story line

Playing with Infinity: Mathematical Explorations and Excursions by Rózsa Péter – High school on up level, but starts at the beginning with addition concepts building up to infinity for older readers / adults. Nice explanation of negative numbers.

Speed Mathematics Using the Vedic System by Vali Nasser – not a reader, but some very interesting ways to look at multiplication and division