I, too, most appreciate what we know as the Socratic method of teaching. It's important to teach young people to think and reason and analyze, and that's generally difficult to do unless it is by design. Some of my greatest moments in teaching have come from these kinds of stimulating discussions. That process, to me as a teacher, is the legacy of Socrates.
I appreciate his legacy in terms of what he taught us about reasoned argument and debating and creative thinking. What is crucial for us to learn from his legacy is ensuring that when we consider big issues we consider them from as many perspectives as we are able to understand before we make a decision. His impact upon Western thought is immense and I would hesitate to begin to quantify it. He is also famous of course for committing suicide by drinking hemlock - perhaps not something to be replicated!
The mark Socrates has left on this world is legendary. He is known as a man who just wouldn't stop asking questions. This attitude led him to become a mentor to some of the world's other biggest thinkers during that era.
I employ a method in my classroom called Socratic Seminar based after Socrates' habits. I like him because his style of thinking is not just accepting a fact at face value and holding it as truth. He asks questions to get mutliple perspectives and considers all approaches. This has led to a very appreciated American value - having an open-mind. You can see this throughout all our founding documents, our history's effort to ensure equalities, and even in the world today as people want acceptance for their ideas or practices that are outside the mainstream.
Socrates would accept all of that. He would claim that all information or new insight futher develops our body of knowledge. The only criticism I would have of Socrates is that I wonder at which moments a person would know for sure when a quest for knowledge about a particular topic has ended.