Advanced Avionics Handbook. Just-published guide to glass cockpit technology, autopilots, moving maps and so on. While most of the JAR PPL syllabus is still rooted in 20th century technology, it’s impressive that the FAA is looking forward.
Instrument Procedures Handbook. Advice on IFR operations such as SIDs and STARs. Much more focused on real operations than on training. Very helpful.
Instrument Flying Handbook. A good introduction to the skills needed for an instrument rating.
Pilot’s Handbook of Aeronautical Knowledge. An encyclopaedic guide to topics such as aerodynamics and other useful information needed for FAA exams and safe flying.
Plane Sense. Information you need to know if you are going to buy and operate your own aircraft but also stuff that is regularly tested on exams like mandatory documents and the responsibilities of pilots.
Risk Management Handbook. With many GA accidents occurring after pilots pass their PPL but before they build up a good body of experience (the gap sometimes called “the killing zone” after the book of the same name), this handbook is a helpful introduction to risk management and aeronautical decision-making.
(Hat tip: Aviation Mentor)