Paul writes to Timothy: By rejecting conscience, certain persons have suffered shipwreck in the faith (1 Tim 1.19).
God was very wise when he created the world and human persons. He gave humanity the faculty of conscience, so that we could have direction and guidance within our very selves as to how we ought to act. Our conscience tells us when something we are considering (or perhaps have already done) is bad; on the other hand, it also prompts us to do things which are good, which nevertheless may be difficult in some way or another. In any case, it is essential to a healthy human life lived according to the design plan of God that human beings follow conscience.
What a danger, then, when a person ignores conscience! It is worse still if a person should turn off their conscience, shutting its voice for good. At that point, the final power for good that God has put in a person is gone, and there is no more restraining the expression of the evil within. You may listen to other persons' advice and moral remonstrances, but only if you have a conscience yourself. If you lose your conscience, and in this way lose any connection or understanding with those who would advise you to act differently, you will have no reason to follow them. There will be no more impulse for good working within you, but only the impulse for evil.
If you manage to do this, you are certain to destroy your faith. A person cannot go on believing in God if he lives as if there are no reasonable and authoritative boundaries on his behavior. Plotinus once said that without virtue, God is merely a word. That is exactly right, and Paul shares the same sentiment here when he writes to Timothy. Those who ignore their conscience -- which is God's voice within them, telling them that they ought to live differently -- have cut themselves off from God and from his truth. What faith is left for them? What can they believe in, who reject God's voice and his commands?
On the other hand, it is the testimony of not a few persons that, during the process of becoming Christians, they experienced a reactivation of their consciences. Once more, for the first time in a long while if not ever, they felt that the lives they had been living were wrong. They heard the voice within them telling them that what they do is not right, that they are guilty of sin.
In these ways, we can see that conscience is a tool of which God makes use to bring human beings to salvation. It is vitally important to hear its voice, to heed its directions and guidance.
We can go about this a different way, too. For myself, I find it preferable to live a life with as few troubles and worries as possible. That is simply the way I enjoy to go through my days -- not worrying so much. Why should I pile on to all the other troubles which life inevitably brings, this particular trouble of my own making -- that of disobeying my conscience and incurring the sentiments of shame and guilt which follow thereupon? Why shouldn't I save myself from a trouble that depends entirely on me and no one else?