Even in the Church age of grace, obedience is still an essential part of serving the Lord. The importance of obedience is illustrated in I Samuel 15:22 where the prophet says, "Behold, to obey is better than sacrifice, and to hearken than the fat of rams." The Lord would rather have us be obedient to his given commands than to offer up sacrifice. He would rather have us listen than to offer the best part of a sacrifice.
In the New Testament, we find that obedience is essential. Jesus said, "Why do you call me 'Lord, Lord,' but you don't obey me?" (Luke 6:46). Peter said that the Lord gives the Holy Ghost to those that obey Him (Acts 5:32). Paul wrote to the Thessalonians saying that when the Lord returns, He will take vengeance on those that don't obey the gospel (II Thessalonians 1:7-8).
Often people don't obey because they don't see an immediate effect or result to their obedience. The battle of Jericho is an example that shows that the effect of obedience isn't always immediate. The children of Israel were told to silently march around the walls of Jericho 13 times. Nothing happened the first 12 times they marched, but on the 13th time when they shouted as they were told to shout, the walls tumbled down. The effect of obedience isn't always immediate, but obedience will always eventually bear fruit. Blessed is the man that fears the Lord and delights in His commandments (Psalm 112:1).