I remember the illustrations of these more than the stories. Black-and-white pictures of two little girls with their hair in pigtails. Betsy had black hair and wore dresses to school every day (weird). The series began with B is for Betsy, which was published in the 30s, and it seemed delightfully old-fashioned to me. It was around fifty years old when I read it.
The one story that I remember clearly was when Betsy's parents decided that she and her little sister could have a dog. (I think it was from B is for Betsy.) But, oh no, they each want a different kind of dog! How will they decide what to do? Each girl is picturing her perfect dog, already loving it, her heart about to break if she can't get that dog.
And then, (spoiler but you know, almost 100 years old), her dad just goes and gets them two dogs. TWO DOGS. They each get the dog that they wanted. They were outside in their yard, I believe, and their dad called to them, and they turned around to see the two puppies running down the hill to them. I think that's how it went; it's how I can still see it clearly in my mind. I was amazed. Two dogs. This Betsy girl lived a charmed life, in my opinion.
I remember being very taken with Snowbound With Betsy. We didn't get much snow, so being snowed in for days, as they were in the story, fascinated me. The title Betsy and the Boys and Betsy's Winterhouse also sound familiar.
A few years ago, something made me remember one of those black-and-white illustrations, and I tried looking Betsy up, only to find pages of links about Betsy-Tacy. These books were not even on my radar when I was a kid. But apparently they were extremely popular.
While I was poking around online, I saw some reviews of the books in which parents warn that the children in the books are allowed to walk around alone and talk to strangers. There may be some edited versions in which outdated and objectionable language is cleaned up. So, if you are thinking of reading one of these aloud to a little one, go through it first and see if there are any edits or explanations that you need to make.