Mormon 9:29

See that ye are not baptized unworthily; see that ye partake not of the sacrament of Christ unworthily; but see that ye do all things in worthiness, and do it in the name of Jesus Christ, the Son of the living God; and if ye do this, and endure to the end, ye will in nowise be cast out.

Proper actions are important. Proper actions for the right reasons are essential. To serve God most effectively, we must be in tune with the Holy Spirit so we can receive guidance and direction, and therefore we must be worthy. Worthy does not mean perfect, but it means that we are trying in humility, constantly repenting. To act in the name of Christ is to do what he would do the way he would do it for the reasons he would do it. That takes revelation, and revelation comes only to those who are worthy.

3 Nephi 18:29

For whoso eateth and drinketh my flesh and blood unworthily eateth and drinketh damnation to his soul; therefore if ye know that a man is unworthy to eat and drink of my flesh and blood ye shall forbid him.

Let's be clear: no one is worthy to partake of the sacrament. We come to the sacrament table in introspection and repentance, acknowledging that we failed to keep our covenants perfectly during the preceding week. We renew our covenants of the sacrament weekly because weekly we fall short of our desires to be faithful and righteous. Therefore, to partake worthily does not mean to be without sin but to be without hypocrisy. We partake worthily when we truly want to keep the covenants we make and are willing to strive to be obedient. The point of the sacrament is not to be perfect but to have the intent to become perfect through the continuous atonement of Christ.  Jesus warns his disciples about those who partake of the sacrament for show or to be socially acceptable or to hide rebellion and intentional sins. For such, the sacrament is a curse rather than a blessing. If one does not intend to keep the covenants, it is best that he not pretend to make them in the first place. For the rest of us, we just have to keep trying.

Alma 38:14

Do not say: O God, I thank thee that we are better than our brethren; but rather say: O Lord, forgive my unworthiness, and remember my brethren in mercy—yea, acknowledge your unworthiness before God at all times.

It is tempting, when things are going well, to want to think that we ourselves are somehow responsible for the good things that surround us. We may work, and we may see fruits of our labors. But we should never think that we have earned a blessing or that we are entitled. We ourselves are never truly worthy of the blessings God chooses to give us. He gives gifts, not because we have purchased them with our righteousness, but because he loves us and wants to help us. When we remember our unworthiness, especially in the face of continued blessings, we keep things in perspective. At the center of that perspective is Christ and his atonement.