Did Jesus's teachings replace those of the Old Testament?

I've been thinking about this a lot lately. Many teachings of the Old Testament such as 'an eye for an eye' seem to oppose the teachings of Jesus, who preached unconditional love, non-judgement, non-violence and forgiveness. Also, many morally questionable concepts such as punishment, war, animal sacrifices, and cursing seem so evident in the O.T. and appear to be denounced in the N.T. In addition, if Jesus did indeed "override" or revise the concept of God and moral law of the O.T., then why is it still taught in churches today as lessons to follow? Shouldn't the teachings of the O.T. be conveyed as the old ways, and not the basis for any true Christian's beliefs or perceptions (both spiritual and social)?