Like several others on here...Little Women. It transported me to an earlier time that, though very different from my own adolescence, captured me completely. I followed it with the other books in the series including Little Men, Jo's Boys.
This has reminded me...I struggled to learn to read. With the help of a lovely teacher I finally cracked it and became a voracious reader. I borrowed so many books from the school library, they thought I wasn't actually reading them. Mostly books about animals...horses and dogs. A treasured book of my own was Lad, a Dog...by Albert Payson Terhune. A collection of short stories about his own beloved rough collie. Written in 1919 it probably started my campaign for a dog of of my own.
Amazon.co.uk User Recommendation
Obviously both are childhood favourites...its more difficult to pick more recent ones.
I'll have a think...