If you know a great book that's not on this list, feel free to suggest!
Clayden, Greeves, Warren, Organic Chemistry, 2nd ed. The best organic chemistry textbook. Period.
Zweifel, Nantz, Modern Organic Synthesis: An Introduction. A great collection of the most important reagents and synthetic transformations, neatly organised and easy to memorize. Popular in the US but suprisingly difficult to find in the UK. It is a practical companion to the "Claiden", the latter being focused more on theory. The second edition of the Zweifel-Nantz is due to come out in 2017.
Myers, Organic Chemistry Handouts. Phenomenally useful handouts on various topics of synthetic organic chemistry.
Anslyn, Dougherty, Modern Physical Organic Chemistry. The definitive textbook on physical organic chemistry. The text is captivating but at times too long.
Grossman, The Art of Writing Reasonable Reaction Mechanisms. Great introductory book on how to do arrow pushing in organic chemistry. It focuses on "paper mechanisms", rather than the study of the flask contents, and thus requires the Anslyn-Dougherty for a complete picture.
Wyatt, Warren, Organic Synthesis: The Disconnection Approach. A primer on retrosynthetic analysis.
Crabtree, Organometallic Chemistry of Transition Metals, 4th ed. The 4th edition is possibly the best organometallic chemistry textbook ever written. Really easy to understand by a "mainstream" organic chemist. The 6th edition is for some reason re-written and became much worse.
Kurti, Czako, Strategic Applications of Named Reactions in Organic Synthesis. A great handbook of name reactions. By no means comprehensive (e.g. it lacks the Appel reaction) but still a must-have.
Greene, Wutts, Protective Groups in Organic Synthesis. An exhaustive list of protecting groups with convenient listings of protecting/deprotecting conditions.
Kocienski, Protecting Groups. An equally great book to complement the Greene-Wutts. An added bonus – characteristic NMR peaks of the discussed groups.
Joule, Mills, Heterocyclic Chemistry. Introductory textbook on heterocycles. However, the desire of authors to include as much information as possible led to often boring text.
Baran, Heterocyclic Chemistry. This is a video course available on iTunes U. Perhaps the best heterocyclic chemistry lectures – and definitely the toughest I have seen.
Fleming, Molecular Orbitals and Organic Chemical Reactions. All you need to know about molecular orbitals. There are two editions of this book: a comprehensive (and sometimes boring) Reference Edition and a concise Student Edition.
Patrick, An Introduction to Medicinal Chemistry. A fantastic introductory text on medchem. Occasional witty British humour.
Lee, Robinson, Process Development. An Oxford Chemistry Primer on process chemistry. Helps develop a different prospective on a reaction.
Nicolaou et al, Classics in Total Synthesis, Vol. 1-3. A fantastic collection of the most important, or otherwise instructive, total syntheses. Most of chapters highlight a specific aspect of organic chemistry or trace the differences in various groups' tactics.
Strategies and Tactics in Organic Synthesis, Vol. 1-14. A multi-volume series, published over the last 30-odd years. Chapters are written by those who performed the actual syntheses and thus contain a lot of behind-the-scenes material.
Meeting/seminar notes: Baran, Burke, Columbia, Denmark, Evans, Kanai, MacMillan, Stoltz, White... See my Chemistry Links page.
Carey, Sundberg, Advanced Organic Chemistry. A great textbook which has largely been superceded by more recent texts and online lecture notes.
Hudlicky, Wernerova, The Way of Synthesis. An attempt to draw a broad picture of the organic synthesis. Some chapters are truly unique and cover material not found elsewhere.
Sierra, de la Torre, Dead Ends and Detours. An unusual book that cover a topic usually ignored – failed synthetic approaches and means to overcome them.