During the slow pace of part 61 training I've heard the best thing an aspiring pilot can do is suck up as much knowledge as possible and get his or her hands on as many aviation related books as possible. Below are the core books I've used in my training. Given that my Private ticket took 13 years, those listed are mostly for the instrument rating (with a couple exceptions.) Let me know if you have any that aren't here?
'Fate is the Hunter' Ernest Gann
Fantastic and engaging writing, and a great motivator for those who look to the airlines for a career in aviation, as well as motivation to be vigilant in the air; "Those 20 feet off the assigned altitude were bothering me..."
'Flying IFR' Richard Collins
Sort of like having that salty old instructor / grandfather tell you how it is, and how he does it, and so should you too...got it? Very helpful, insightful, and his vast experience is essential for us low-timers. The one thing I now think about constantly in the air is 'the needles have to be somewhere, they might as well be in the right place.'
The FAA suite (each pdf is linked, although i suggest buying them bound.)
Basically the government's (free) prescribed way of being a pilot. Essential basics, everything you need to pass the written exams, definitely governmental (i.e. dry, to the point.):
Airplane Flying Handbook
Pilot's Handbook of Aeronautical Knowledge
Aviation Weather Services
Instrument Flying Handbook
Instrument Procedures Handbook
'Jeppesen Instrument Commercial Textbook'
A monolith of information. This is basically the FAA instrument books, but written with character, and made easy to digest. There are pictures, interesting side-stories, quizzes, trivia, and it covers both NACO and Jeppesen charts / plates. Essential for anyone following a career path (i.e. instrument -> commercial).
'Weather Flying' Robert Buck
If the FAA's 'Aviation Weather' is too dry for you (it will be) then pick up this one. It's insightful, and it improved the way i think about big picture weather. Plus this guy has flown thousands of hours in 747's. Awesome.