The Bible is a progressive revelation. If you skip the first half of any good book and try to finish it; you will have a hard time understanding the characters, the plot, and the ending. In the same way, the New Testament is only completely understood when it is seen as being built upon the foundation of the events, characters, laws, sacrificial system, covenants, and promises of the Old Testament. If we only had the New Testament, we would come to the gospels and not know why the Jews were looking for a Messiah (a Savior King). Without the Old Testament, we would not understand why this Messiah was coming (see Isaiah 53); we would not have been able to identify Jesus of Nazareth as the Messiah through the many detailed prophecies that were given concerning Him (e.g., His birth place (Micah 5:2); His manner of death (Psalm 22, especially vv. 1,7-8, 14-18; Psalm 69:21, etc.), His resurrection (Psalm 16:10), and many more details of His ministry (Isaiah 52:13.; 9:2, etc.).
Without the Old Testament, we would not understand the Jewish customs that are mentioned in passing in the New Testament. We would not understand the perversions the Pharisees had made to God’s law as they added their traditions to it. We would not understand why Jesus was so upset as He cleansed the temple courtyard. We would not understand that we can make use of the same wisdom that Christ used in His many replies to His adversaries (both human and demonic).
Without the Old Testament we would miss out on numerous detailed prophecies that could only have come true if the Bible is God’s word, not man’s (see the major and minor prophets) (e.g., Daniel 7 and following chapters). These prophecies give specific details about the rise and fall of nations, how they will fall, if they will rise again, which powers would be next to emerge, who the major players would be (Cyrus, Alexander the Great, etc.), and what would happen to their kingdoms when those players died. These detailed prophecies are so accurate that skeptics charge they had to have been written after the fact.
The Old Testament also contains numerous lessons for us through the lives of its many fallible characters. By observing their lives we can be encouraged to trust God no matter what (Daniel 3), and to not compromise in the little things (Daniel 1) so that we will be faithful later in the big things (Daniel 6). We can learn that it is best to confess sin early and sincerely instead of blame-shifting (1 Samuel 15). We can learn not to play with sin, because it will find us out and its bite is deadly (See Judges 13-16). We can learn that we need to trust (and obey) God if we expect to experience His promised-land living in this life and His paradise in the next (Numbers 13). We learn that if we contemplate sin, we are only setting ourselves up for committing it (Genesis 3; Joshua 6-7). We learn that our sin has consequences not only for ourselves but for our loved ones around us and conversely that our good behavior has rewards not only for us but for those who are around us as well (Genesis 3; Exodus 20:5-6).
The Old Testament also contains vast quantities of wisdom that the New Testament does not share. Many of these are contained in the Psalms and Proverbs. These bits of wisdom reveal how I can be wiser than my teachers, what various sins will lead to (it helps us to see the hook that the bait is hiding), and what accomplishments in this world hold for us (nothing!). How can I recognize whether I am a fool (moral fool, that is)? How can I inadvertently turn people off without trying? How can I open doors to lasting success? How can I find meaning in life? Again, there is so much there that is just waiting to be found by one who truly wants to learn.
Without the Old Testament, we would not have a basis for standing against the error of the politically correct perversions of our society in which evolution is seen to be the creator of all of the species over millions of years (instead of them being the result of special creation by God in a literal six days). We would buy the lie that marriages and the family unit are an evolving structure that should continue to change as society changes, instead of being seen as a design by God for the purpose of raising up godly children and for the protection of those who would otherwise be used and abused (most often women and children).
Without the Old Testament, we would not understand the promises God will yet fulfill to the Jewish nation. As a result, we would not properly see that the Tribulation period is a seven-year period in which He will specifically be working with the Jewish nation who rejected His first coming but who will receive Him at His second coming. We would not understand how Christ’s future 1,000-year reign fits in with His promises to the Jews, nor how the Gentiles will fit in. Nor would we see how the end of the Bible ties up the loose ends that were unraveled in the beginning of the Bible, how God will restore the paradise He originally created this world to be, and how we will enjoy close companionship with Him on a personal basis as in the Garden of Eden.
In summary, the Old Testament is a mirror that allows us to see ourselves in the lives of Old Testament characters and helps us learn vicariously from their lives. It sheds so much light on who God is and the wonders He has made and the salvation He has wrought. It shares so much comfort to those in persecution or trouble (see Psalms especially). It reveals through repeatedly fulfilled prophecy why the Bible is unique among holy books—it alone is able to demonstrate that it is what it claims to be: the inspired Word of God. It reveals volumes about Christ in page after page of its writings. It contains so much wisdom that goes beyond what is alluded to or quoted in the New Testament. In short, if you have not yet ventured in depth into its pages, you are missing much that God has available for you. As you read it, there will be much you do not understand right away, but there will be much you will understand and learn from. And as you continue to study it, asking God to teach you further, your mining will pay off in brighter treasures still.