For whatever was written in former days was written for our instruction, that through endurance and through the encouragement of the Scriptures we might have hope. (ESV)
I have encountered people who were of the opinion that the Old Testament was no longer useful for the modern day Christian. After all, we are part of the new covenant in Jesus Christ. We are no longer under the obligation to fulfill the ceremonial law. Why should we bother with the Old Testament at all? Paul effectively answers that concern in this verse.
The things written in former days was for our instruction. Paul is speaking specifically of the Old Testament. The Apostle Paul was certainly aware that our salvation was now to be received by grace through faith. He knew that by keeping the works of the Law no one would be saved. Yet, that reality did not negate the usefulness of the truths found in the Old Testament.
One of the facts that we need to bear in mind is that, "Jesus Christ is the same yesterday and today and forever. (Hebrews 13:8)" Jesus Christ was present in the Old Testament as well as the New Testament. The sacrificial system was all about Jesus Christ. As the priest sacrificed a lamb for the sins of the people he looked forward to the true lamb of God who was yet to come into the world.
Another thing that we need to realize is that the Old Testament tells us all about the character and nature of the wonderful God that we serve. Is he faithful? Read story after story of his faithfulness. Is he loving? There are accounts that tell of his great love for his people. Is he the judge of all unrighteousness? The scriptures prove this fact again and again.
Maybe it has been a while since you have read from the Old Testament. Consider a reading plan that includes the great truths of the Old Testament. As you read, ask the Holy Spirit to show you the timeless truths of who God is.