James Gleick, Chaos: making a new science (Penguin Books, 1988). A highly-readable and popular book. Makes much of the "scientific revolution" aspect of fractals and chaos.
Ian Stewart, Does God Play Dice? (Blackwell 1989). A popular but more mathematical account of fractals and chaos.
Benoit Mandelbrot, The Fractal Geometry of Nature (Freeman 1982). The book that started it all. Very interesting with lots of material, but often hard to understand in depth.
Peitgen, Heinz-Otto et al, Fractals for the Classroom (2 vols, Springer 1992). A text written for high-school teachers and students. Packed with interesting ideas. The second volume is more technical.
Robert Devaney, A First Course in Chaotic Dynamical Systems (Addison-Wesley 1992). An undergraduate-level text on the mathematics of discrete dynamical systems; ends with Julia sets and the Mandelbrot set.
Heinz-Otto Peitgen and Peter Richter, The Beauty of Fractals (Springer 1986). A summary of what was known about mathematical fractals in 1986, but without proofs. Many color pictures.
Heinz-Otto Peitgen and Dietmar Saupe (ed), The Science of Fractal Images (Springer 1988). Articles by Voss and Saupe (random fractals), Devaney (iteration and Julia sets), Peitgen (Julia sets and the Mandelbrot set), and Barnsley (iterated function systems). Also a description of the algorithm of Milnor and Thurston to draw the Mandelbrot set. Many fine pictures. The level is more elementary than Peitgen and Richter.
Michael Barnsley, Fractals Everywhere (Academic Press 1988). An undergraduate text about iterated function systems. Contains an introduction to point-set topology and lots of exercises.
Nina Hall (ed), Exploring Chaos (Norton 1991). A collection of essays for the non-specialist from the magazine The New Scientist.
Jens Feder, Fractals (Plenum 1988). A more mathematical book on fractals in the sciences. Well-written.
Michael McGuire, An Eye for Fractals (Addison-Wesley 1991). Brief mathematical descriptions of various fractals are followed by photographs of similar-looking objects in the natural world. Thought-provoking with good photographs.
Eliot Porter, Nature's Chaos (Viking 1990). Sierra-Club-type photographs of natural objects which look like fractals. Some text by Gleick.
Etienne Guyon and H. Eugene Stanley (ed), Fractal Forms (Elsevier 1991). Pictures of fractals in nature. (The captions are at the end of the book.)
John Briggs, Fractals, the Patterns of Chaos (Touchstone 1992). Brief descriptions of fractal and chaotic phenomina with many fine pictures.