A Brief History of Time - Stephen Hawking
Published in 1988, I just flipped through it to see if it's too dated, but he ends with a discussion of string theory and I think this one should count as a classic.

The Language of the Genes - Steve Jones
Published in 1993, way before the human genome was sort of fully mapped, Jones communicates the science through a beautifully written account of the ways in which the evolution and shuffling of genes have shaped human lives.

I would second the nomination of Bill Bryson's Short History of Nearly Everything - well-known for writing travel books, he took 3 years to research this entertaining and pretty accurate overview of scientific knowledge.

Please visit my new blogsite where I've started to review books like:

Oxygen: the molecule that made the world - Nick Lane
which tells a brilliantly convincing story of how protection from oxygen free radicals and aerobic metabolism might have evolved in early life forms before photosynthesis itself.

- iid noise
www.bloglikelihood.blogspot.com