A few months ago, I taught an Old Testament survey class at my church. I was asked to answer the question: What does the Old Testament have to do with me? ... A valid question in a "New Testament church." Many Christians today know that the Old Testament is important, but may not be able to explain why. So here was my response:
1) The Old Testament completes our undersanding of how God has been working toward His ultimate goal.
(See my previous few posts for the context of this answer. In a nutshell, God's ultimate goal is to have an intimate relationship with a group of people.)
We live in a certain point of time in history. Understanding how God has worked in times past helps us understand the big picture and where we fit in that picture. Although the character of God never changes, the way that He works in the world does. For example, how he was working during the time of Abraham was much less dramatic than how he was working during the time of the Exodus. And His commands to Joshua were vastly different than His commands to the apostles. By studying the Old Testament, you can begin to grasp the big picture of how God is accomplishing His goal.
2) The Old Testament teaches us about God's character.
Much of the Old Testament is devoted to a discussion of God's character. During the time of Moses (Genesis through Deuteronomy), God had to introduce Himself to the Israelites, explain who He was and what He demanded of them. The narrative books after the time of Moses (Joshua through Esther) tell us how God interacted with his people over the course of about a thousand years ... both the blessings and the curses. The next section of the OT (Job through Song of Solomon) teaches us about God's charater through poetry. And in the prophets (Isaiah through Malachi), God was sending direct messages to His people and surrounding nations about His holy standards. Granted, this is an oversimplification, but you get the point. Our knowledge about God's character would be greatly reduced if all we had was the New Testament.
3) The Old Testament lays the foundation for the New Testament.
Throughout the New Testament, the Old Testament is alluded to either directly or undirectly an uncountable number of times. The NT writers lived in the New Testmant period, but were firmly grounded in the Old Testament scriptures. It would be impossible to fully understand and appreciate the New Testament if we did not have the Old Testament.
4) The Old Testament is filled with godly examples for our lives.
There is no denying the fact that many of the stories in the Old Testament are downright inspring. Men like Abraham, Moses, Joshua, David, and Daniel faced incredible situations and through faith in God triumphed against the odds. As Rich Mullins once sang, "stories like that make a boy grow bold; stories like that make a man walk straight" ("Boy Like Me, Man Like You"). The Old Testament saints were just as frail and just as human as the rest of us. But they had a real faith in a real God despite the fact that they faced real problems. We can learn a lot from their examples and can find the courage to face our own trials.
This is by no means an exhaustive list. If you think of some more, attach a comment or send me an email. I've only recently begun crystalizing my thoughts on this issue.