I was reading fluently by the age of three, and the first books I remember are the ones so many children remember starting with: Dr. Seuss.
Not Green Eggs and Ham, though. I never liked that one. Later, I would use Green Eggs and Ham to teach my best friend (four years my junior) to read, but for myself, I remember There's a Wocket in My Pocket and I Can Read with My Eyes Shut! to be my favorites. I thought The Cat in the Hat was okay, and of course One Fish Two Fish Red Fish Blue Fish, but Mr. Brown Can Moo! Can You? topped them, I think. At least in my young mind.
I recall the cartoons, too. Not just Grinch at Christmas, but The Cat in the Hat where he sings: "Cat. Hat. In French, chat, chapeau . . ." (For the record, I cannot stand that new Cat in the Hat cartoon series; I find it truly obnoxious and the very antithesis of the original story.) And the cartoon version of The Lorax, and The Sneeches . . .
Of course, I can't really think about Seuss without also thinking about Eastman and Go, Dog. Go! I spent a lot of time looking at that page with all the dogs having the party in the tree.
And then there was Ten Apples Up On Top! Which had Theo. LeSieg's name on it, but I guess was really Dr. Seuss all along.
When I got too old for these books, I put them in one of my parents' military lockers. They stayed there for years. And then I had kids of my own, and now they read the same books I did. They didn't learn to read as early as I; I don't know what made the difference. Maybe the fact I was an only child and they have each other to play with. I spent so much time alone and reading, but they don't have to. They do love to read, but they do it as a social activity more than a solitary one. They read to each other, or like us to read to them. Whereas for me reading will always be a quiet thing I prefer to do alone.