The First Three Minutes, by Steven Weinberg (1977).
An excellent popular account of the big bang theory, primordial nucleosynthesis, the microwave background, and so forth, by a Nobel prize winning physicist. Similar subject matter to the end of this course, but more depth and history. I read it many years ago and liked it a lot.
The Light at the Edge of the Universe, by Michael Lemonick (1993).
A popular account of current research in cosmology --- dark matter, the very early universe, large-scale structure, the formation of galaxies, and so forth. Goes beyond what this course covered, but at an easily accessible level. Lemonick is a science reporter, and he is especially good at explaining the observational side of cosmology. I was the science fact-checker for the book, so I read a pre-publication draft very carefully, and I thought it was quite good.
First Light, by Richard Preston (1987).
Focuses on two long-term science projects at Palomar Observatory: a search for distant quasars, and a search for comets careening around the solar system. Preston is a superb writer (his recent best-seller is The Hot Zone), and this book probably gives the best feel of any about what observational astronomy is like in real life. It gives a great portrait of the people involved in these projects, one of them my thesis advisor, Jim Gunn. It is probably makes the most engaging reading of any of these books, but it covers the smallest amount of scientific ground. I read it several years ago and loved it.
Coming of Age in the Milky Way, by Timothy Ferris (1993?).
I haven't read this book, but I have heard it highly recommended. I like other stuff that I have read by the author; he's usually quite accessible but also accurate.
Black Holes and Time Warps: Einstein's Outrageous Legacy, by Kip Thorne (1995?).
A popular description of general relativity and various of the bizarre phenomena that it predicts, by one of the leading theorists in the field of general relativity. I haven't read the book, but I've heard that it's good, and it made it to the New York Times bestseller list. It may be a bit on the technical side.
Mr. Tompkins in Wonderland, by George Gamow.
This lighthearted book illustrates relativity by imagining towns where fundamental physical constants are very different (e.g., the speed of light is 60 miles/hour) and describing Mr. Tompkins's adventures there. I think its most recent reprinting is in a collection titled Mr. Tompkins in Paperback, which combines it with another of Gamow's Mr. Tompkins books that does similar things for quantum theory.
Einstein's Dreams, by Alan Lightman.
This is a work of fiction, in which Lightman invents a series of dreams about time and space that he supposes Einstein to have had as he was struggling to arrive at his theory of relativity. It was on the New York Times bestseller list for many weeks, and I found it eloquent and clever.