Yes, they do.
The district puts out a packet, and the goal is for them to complete the packet.
Last year for the 2nd going into 3rd graders had to do a few things.
They had to read a biography, science, nature, and something else. They they had to read about 5 fiction books. (it all equaled out to 10 substantial books)
They had to do a story map, plot map, personal narrative, and something else with it.
In his packet, there was also four personal letters he had to write as well.
My duaghters K/1 pack was extremely easy. It was read 10 books and draw pictures with it.
No, it did not affect their grades if they did not do it. But they did get a picnic/ice cream party if they did do it.
In my middle school, the students can get one of a few books to read for the 6th graders it was Bridge to Teribatha, Tangerine, some war/helicopter one, Song of Dolphins, and one more. An alternate selection for the lower reading level was Holes.
They had to use this book, and keep a journal about it. In essence they had to use sticky notes to keep notes about it. In the first month or so of school they did a project on it. In truth, you didn't really NEED to read it over the summer, but you would be busting your butt to complete the book and the project before time was up for the project.