Physics
Problems in General Physics, I.E.Irodov, MIR Publishers, Moscow
This is probably the best collection of problems of all hues in elementary Physics. I have spent many an engrossing and thoroughly enjoyable hour grappling with the famous "Irodov" problems.

Mathematics
Problems in Calculus of one variable,  Isaac Baron, MIR Publishers, Moscow
A Problem Book in Mathematical Analysis, G.N.Berman, MIR Publishers, Moscow
The USSR Olympiad problem book, N.D.Chentzov, Dover, USA

These books primarily deal with problems in elementary mathematics that do not need more than high school knowledge to solve. However, the problems are tough in the sense that they need "unconventional" approaches. If you are in India, you are in luck as the most useful MIR books are republished by CBS Publishers and Distributors.

Good Writing
The Elements of Style, Strunk & White, Allyn and Bacon, USA
This is a timeless classic on good writing. I've found it exceptionally useful. Available for download from here.

Fowler's Modern English Usage, Gowers, Oxford University Press, United Kingdom
For folks who care about using the Queen's English !

General Science
Godel, Escher, Bach : An Eternal Golden Braid, Douglas R. Hofstadter, Basic Books, USA
GEB needs no introduction.

The Astonishing Hypothesis, Francis Crick, Simon & Schuster, USA
This book talks about the scientific search for the human soul. The author won the Nobel prize for deciphering the structure of the DNA.

How to Solve It, George Polya, Princeton University Press, USA
A perennial book which captures Polya's deep insight into the mathematical method.

A Mathematician's Apology, G.H.Hardy, Cambridge University Press, UK
A brilliant account of mathematics.

Generalia
India's Nuclear Bomb, George Perkovich, University of California Press, Berkeley, USA
Perkovich presents a reasonably accurate factual account of the story of India's nuclear bombs interspersed with seemingly dispassionate analysis.