Pie Rats, Ahoy!
That was very, very popular in my house.
My son used to follow me and beg me to read about Uncle Willy- I once read that book 9 times in a row! DS was very speech delayed and when he began to talk at 2 1/2, he began by repeating the whole story. 
Slightly OT, I know, but For modern collaborations, two mentions:
I’m really ejoying reading the books of Julia Donaldson & Axel Scheffler to my toddler. Light, fluffy, but *great *to read aloud. The Gruffalo is going to be an all-time classic along with Wild Things or Goodnight, Moon.
For myself, the YA works of Paul Stewart & Chris Riddel are great - brilliant, dark writing and perfectly complementary, detailed line drawings. The Deepwoods stuff is great, although no-one else on the 'Dope seems to have heard of it. Fantasy fans definitely should.
On another sidenote:
I’ve just gotten Maurice Sendak’s essay/speech collection - he writes about illustrators that inspired him, makes good reading.
I have a couple of them up in a closet right now. Most of my other childhood toys were donated or tossed, but I couldn’t part with these. I had no idea they were so rare.
If we’re going that way, I nominate Gahan Wilson! 
(I thought of him in this connection based on his “Nuts” strip (long-running in the late, lamented National Lampoon), which is about kids rather than for them. But it turns out he’s also done children’s books.)
Did she do her own illos?
Since we’re bringing in other authors, I’ll give a mention to Laura Ingalls Wilder and Lewis Carroll. Both of them wrote books that are now classics.
I’d give the nod to Dr. Seuss, for innovative style, both as to the writing and illustration. I agree about Richard Scarry – the miniaturism appeals (though not my own kids so much), but if I had to venture a guess, I’d say his appeal is more to boys and less to girls. Anybody have any confirmatory thoughts?
The Bernsteins, definitely their early work was better and zippier. When they began cranking out one moralizing thing after another, they just became tiresome. The lack-of-names issue mentioned above bugs me a tiny bit, too. I think the Bernsteins fell into this accidentally (it’s a bit of an artifact of He Bear, She Bear, it seems to me), and got trapped. These days, alas, I find myself reading more Bernstein Bears than all of the other nominees put together.
Mercer Meyer, all I know is the Little Critter series, which I loathe. Fortunately there are none of those books in my house at present.
I’ll echo Ichbin Dubist in saying that Arnold Lobel is incomparable, among the best ever. I’ll add in Russell Hoban and Garth Williams for the Frances series, which should be at the top of any pile.
One of the pities of Seuss and Scarry is the vast amount of ersatz crap produced out of their names and characters since they died. I’m afraid it’ll have an effect on their legacies, unfortunately.
I don’t have a vote, so, sorry to be breaking the rules, but this is important! No one has yet mentioned (that I noticed) Sandra Boynton. An Amazon author search turns up 1770 hits. She was our fav here while the kids were 3 or so.
Seuss, no contest.
You want intricate illustrations? Read The Sleep Book. Not to mention that the words of The Sleep Book are pure poetry.
Oh yes - some might say the writing is only to frame her watercolours, rather than the other way around. She also did some scientific illustration, and might have made a better scientist than author - she was one of the first people to make the lichen=>symbiote relationship, but sexism and upbringing stood in her way.
Yes, Beatrix Potter was enormously interested in biology, and specialized in fungi. She did experiments and classification on her own–made hundreds of exact drawings over months of research–and was really in a position to make a serious contribution to scientific knowledge, but the gentlemen scientists of the day were pretty much offended by her very existence, so she didn’t get much of anywhere.
It’s very interesting to read about, especially her childhood adventures with her brother–IIRC they collected dead animals (such as foxes), boiled the bones bare, and assembled the skeletons, all in secret.
Huh, I didn’t know she did books, too. I thought she was just greeting cards and the like (I still get a kick out of “Wee fish, ewe, a mare, egrets, moose, panda, hippo, gnu, deer”).
Oh, and back to the OP, I’d never even heard of Mercer Mayer before, and none of his many book titles rung a bell (though I skimmed the list and might have missed one). Very surprising, given how many kids’ books there have always been in my mom’s house.
My favorite was definitely Robert Munsch.
Favorite books include The Paperbag Princess, I Have To Go, Jonathan Clean Up (And Then He Heard A Sound), Thomas’ Snowsuit, Murmel Murmel Murmel, Angela’s Airplane and Mortimer.
My mother was particularly fond of Love You Forever, but it’s a little too cloyingly sweet for me (and a little creepy as well).
Of the people mentioned in the OP, I’d rank Seuss first, Scarry second, and the Berenstains third (their book of panel cartoons, Never Trust Anyone Over 13, was a favorite in the Sternvogel household). Mercer Mayer was “after my time” – I recognize a few of the titles, but I don’t recall reading any of his books, either to myself or to my younger siblings.
Boynton writes great board books for toddlers. But not the Hippopotamus is my personal favorite, but right up there is Moo Baa, La La La.
Scarry appeals more to my daughter as she gets older; she is now three. Seus and Boynton appealed from the start.
Speaking of Dr. Suess, here’s a wonderful filksong by Tom Smith! (To the tune of “500 Miles” by the Proclaimers.)
That was really, really cool. Thanks, man!
Scarry, by a nose. Seuss might have the wackier rhymes and images, but Scarry’s illustrations win it for me.
My son is, unfortunately, really big on the Bernstein Bears at the moment; I don’t mind the occassional “how to live life like a good Bear should” book, but I’m drawing the line at The Berenstain Bears And Poppa’s Nasty Old Bout Of Diarrhea.
Does a bear . . . never mind.