So now that I've relaxed my own criteria, here's my list:

World History

• Atlas of World History by John Haywood (unfortunately out of print): Really excellent for getting a detailed balanced understanding of world history. Also excellent at pointing out causes and effects. Good coverage of political, demographic, and economic history, but very poor for cultural and intellectual history.
• Sapiens by Yuval Noah Harari (LW summary): Some controversial positions presented as accepted fact, but otherwise very good overview of the social science aspects of the history of humanity.

Biology

• The Machinery of Life: Hand-drawn pictures gives an excellent sense of how the cell operates.
• Life Unfolding: How the Human Body Creates Itself
• Your Inner Fish: Good introduction to evolution. Also available as DVD from PBS.

Physics: See here