Excellent (if slightly outdated) book about the history of space exploration by William E. Burrows. Covers the entire history of space exploration, right from Daedalus and Lucian right up to the present-day (of 1997). Focuses especially on the moon race and the American space program, but does contain information about Soviet programs as well.
While it is quite good, the book does have its flaws. It is quite wordy (surprising for a 646-page long complete synopsis of space flight) and has a tendency to backtrack while in media res and start an entirely new "plotline". It also doesn't cover smaller space programs (such as the European, Japanese, Chinese, or Indian programs) very well at all, relegating them to single paragraphs spread throughout the book.
Despite the above, it does have quite a few things going for it. It is (fairly) short for a book covering such an enormous subject; as such, it is practical to actually read it, rather than simply skimming or reading the best bits. It also contains information gleaned from interviews with quite a few personages, including a large number of ex-Soviet space experts. It is fairly readable, with decent (if not spectacular) prose. Finally, it is interesting as a historical artifact. A lot of things, after all, have changed in space exploration since 1998, so it can be quite interesting to compare what people back then thought about the subject to what actually happened, and what people think now.