Marcella Hazan, one of my favorite cookbook authors, once wrote that spices should be used as "as a halo and not as a club." In other words, they should enhance rather than overwhelm a dish.
I believe the same holds true for alliteration. Use it in small doses; employ assonance and consonance as well to mix it up a bit. All three can be combined very effectively in poetry:
"The moan of doves in immemorial elms,
And murmuring of innumerable bees." (Tennyson)
They are usually distracting when overused in prose, however (unless specifically employed as a mnemonic device, such as in a sermon or other didactic piece).
To be honest, I wish more people could sound like Dr. Seuss. What sets his work far above many of his imitators was not his love for alliteration but his strict adherence to his poetic meter of choice. Flaubert wrote, "Poetry is as precise as geometry," and that certainly is true of the writing of Dr. Seuss.
He wrote many of his early books, like And To Think That I Saw It On Mulberry Street, in anapestic tetrameter. What does all that polysyllabic Greek mean?
An anapest is a rhythmic unit, or 'foot,' composed of two unstressed syllables followed by a stressed syllable, as in the word 'underneath' or the phrase 'in the car.' 'Tetrameter' means that there are four feet to each line. Read the title of the book in the above paragraph, and you'll get it. Or, here's Lord Byron: "And the sheen of their spears was like stars on the sea" (and dig that alliteration, baby).
Sometimes Seuss would eliminate the first weak syllable and/or tack one on at the end of a line, as in "In all the whole town, the most wonderful spot," which is the first line of If I Ran the Circus. But this has always been an acceptable adaptation of the meter.
He also wrote in trochaic tetrameter (trochees are feet that have a stressed syllable followed by an unstressed syllable, as in 'doughnut' or 'hard hat'), sometimes mixing it up with iambic tetrameter (iambs are feet that have an unstressed syllable followed by a stressed syllable, like 'begin' or 'to be'). In Green Eggs and Ham, the two main characters have very different poetic voices: once speaks in iambs, the other mostly in trochees.
Whatever his chosen meter, it was flawless, which makes his writing a joy to read out loud. Dr. Seuss would often labor for months over his deceptively simple texts so that he could express the story's ideas and images while maintaining pristine rhythm. My favorite of his is called "Too Many Daves," found in the collection The Sneetches and Other Stories. It's perfect, I tell you, perfect.
Imitators today don't have his discipline and discerning ear; therefore their stories sound clumsy and clunky. I won't name names, but I've read far too many children's books that use poetical meter in a halfhearted sort of way, thinking that an end-rhyme will cover a multitude of sins. Not so.
The Cat in the Hat has sold over seven million copies because even toddlers and their parents who don't know an anapest from a dactyl recognize this formula:
Brilliantly imagined plot and characters + hypnotic, never-stumbling rhythm = story that never gets stale.
(Take it from me, the mother of five Seuss-lovers; I've probably read that book two thousand times in the past fourteen years.)
If you want to create rhythmic, rhyming children's books with that kind of selling and staying power, read Byron and Tennyson and Longfellow and study their meters. Be as precise as a geometer in your content and in your form.
It wouldn't hurt if you could draw fantastical creatures, buildings, and machines in an accessible, instantly recognizable style while you're at it. But that's a subject for a whole other post.