The first and most important book to read is Market Wizards by Jack D. Schwager. This is the most important book for you to read as it has great stories to inspire you and get you interested in the markets.
The second book I would recommend is How I Made 2,000,000 in the Stock Market by Nicolas Darvas. Again, this is a very interesting book written by a non-market man.
The third book I'd recommend after you've read the initial two blockbusters is Trading Rules: Strategies for Success by William F. Eng. This book is about trading itself. It covers everything about technical analysis from Moving Averages to even Astrology! It's a must read - let me warn you it's a serious book.
For my fourth book, I'd like to recommend a book which mostly deals in options trading. The book is called Options as a Strategic Investment by Lawrence G. McMillan and covers most everything you need to know about options. This is a must have for all you option geeks, pardon the pun.
The fifth book is not really a book on trading, it's a book about psychology and you. Psychology professor Mihaly Csikszentmihalyi who emigrated to the US at a very early age has written an excellent, inspirational book called Flow: The Psychology of Optimal Experience which teaches us how to get totally immersed in what we do. This should get you through your difficult trading days.