Keep your kids learning and occupied throughout the summer with a variety of free programs.
PBS Summer Learning: A collection of videos and interactives.
Legends of Learning: This site is providing 10 weeks of free math and science activities that are game-based. They are also running STEM competitions. For grades 1 - 8.
Wide Open School: A collection of online learning sites organized by grade (pre-school through 12) and subject.
Smartpegs: 8 weeks of free science activities
Start with a Book: This site has printable Reading Adventure Packs for grades K - 3, covering a variety of topics, including Bugs, Birds, and Animals; Flight; Time and Time Travel; and others (24 altogether). You'll also find links to hands-on activities, writing prompts, websites and mobile apps.
Things You Wanna Know: NatGeo Kids video series.
Newsela Summer Reading Clubs: For grades 2 - 12, students can join clubs on a variety of interests, including animals, technology, movies, and more.
Explorer HQ: Become an intrepid explorer and complete a variety of unusual missions to earn badges.
Science of Summer: Explore the science behind summer activities at this PBS LearningMedia site. Topics include the physics of sailing, the chemistry of campfires, the science of blowing bubbles, the mineral composition of sand, and the forces that allow humans to ride bicycles and roller coasters.
Maker Camp: Features a collection of projects to make at home.
Camp Wonderopolis: Explore wonders about music and how it relates to other fields, such as science, math and history.
Camp GoNoodle: Each week in July, you receive an email with new adventures and activities, both online and off, and the ability to earn badges.
Self-Learning for Kids: Not really a program, but a very long list of free, self-learning online resources for kids in pre-K through sixth grades. There are 75 resources, organized by type.
(More resources listed in comments sections below)