I think trading books should be broken into categories and I will make this post much more of a list than an actual write up. No affiliate links here just actual good content.
Psychology – think the topic is silly but these are essential
Mark Douglas: Trading in the Zone
Mark Douglas: Disciplined Trader
Alex Elder : Trading for a Living
History – must read for all traders
Jack Schwager – Market Wizards Series
Edwin Lefevre: Reminiscences of a Stock Operator
System Trading – Essentials for success
Murray Ruggerio: Cybernetic Trading Strategies
Larry Williams: Long Term Secrets to Short Term Trading
Emilio Tomasini: Trading Systems
Michael Covel: Complete Turtle Trader
Indicators – I am obsessed
Kirk Northington: Volatility Based Technical Analysis
Perry Kaufman: Trading Systems and Methods (could be in both categories but this bible has every indicator known to man in it)
Other
Nicholas Nassim Taleb: Black Swan