I got A.A. Milne's NOW WE ARE SIX for my sixth birthday, along with a penny charm bracelet and days-of-the-week undies. (I have a very random memory!) I've always had a special fondness for that book, especially King John's Christmas: "But, oh! Father Christmas, if you love me at all, Bring me a big, red India-rubber ball!"
I'm not sure how old I was when I got THE LITTLE SISTER DOLL by Laura Bannon. It was published in 1955, so if I got it the year it came out I was three years old. I still have my copy - well-loved, but a little worse for wear.
Sadly, my books are out of print. That's the way of the book world - and one more reason I like to have old favorites on my shelves.