Yes, the world certainly would be a better place if everyone put the Golden Rule (as it's commonly called) into practice. Jesus' words are just as relevant today as they were when He first spoke them: "In everything, do to others what you would have them do to you" (Matthew 7:12).
But why don't we put it into practice? Why is there so much conflict and evil in the world? The problem isn't ignorance; most people, I suspect, know they ought to treat people with respect and kindness, even if they can't quote Jesus' words exactly. And yet they fail to do it -- and so do we.
The problem is far deeper: The problem is within our own hearts and minds. Down inside, we are selfish and demand our own way -- and this brings us into conflict with others (who are just as selfish). Almost every headline bears witness to this truth. Jesus said, "For from within, out of men's hearts, come evil thoughts, sexual immorality, theft, murder, adultery, greed, malice, deceit, lewdness, envy, slander, arrogance and folly" (Mark 7:21-22).
This is why we need Christ, for only He can take away our stubborn selfishness and replace it with His love and compassion. And He will, as we confess our sins to Him and submit our lives to His control. Don't trust in your own goodness (which has its roots in pride -- which is a sin). Instead, turn to Jesus and commit your life to Him today.