Worship: Broadly and Narrowly Considered
What is the chief end of Man? The chief end or purpose of Man is to glorify God and enjoy Him forever (Westminster Shorter Catechism Question 1). Worship is the giving of glory and honor and praise to God, and it is the goal of our existence. As such, worship is very important for the Christian life.
There is a broad sense in which any life submitted to God is worship. As it is written, "I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship" (Rom. 12:1). In ordinary life, as we live our lives in submission to God with a desire to obey Him and glorify Him, we are engaging in an act of spiritual worship. All Christians ought to be engaging in this broad understanding of worship, and live out the general office of believers in this world.
Narrowly defined, however, "worship" refers to the formal act of explicit praise towards God, and communion with God. Worship narrowly defined is formal and ceremonial. In the Old Testament, the tabernacle and temple services are the places whereby Israel worshiped YHWH. In the worship, praise is offered towards God and God comes down to meet with His people. In the New Testament, worship is now organized around the worship of God and in praise to our Savior Jesus Christ. Arising from a Jewish background, which God intended, worship continues to be the setting whereby men and women can have a covenantal encounter with God, while believers sing praises to God to honor and glorify who He is.
Worship narrowly defined is a religious ritual, thus it has an order to it. Therefore, no matter how "free flowing" and informal a Charismatic service is, by virtue of the fact that it is a religious ritual, it has some kind of a liturgy even if it is unspoken, flexible and ill-defined. The question with regards to worship therefore is not about whether it should be liturgical, but what kind of liturgy should be used and how we get to discern the elements of worship which constitute the liturgy.
Worship: Regulative Principle of Worship
How should we worship? Should we worship God however we feel like it, as long as we do not do anything which God prohibits us from doing? Or should we worship God only in the way He has commanded us to do so? The former is known as the normative principle of worship, while the latter is known as the regulative principle of worship. The Reformed faith in her pure form has held to the regulative principle of worship, noting that God has a lot to command and say about how we are to worship Him especially in the Old Testament. In the New Testament, it is true that the strict laws concerning sacrifices are abolished, and even the place is no more restricted to the tabernacle or the temple at Jerusalem. Rather, we are told to worship "in spirit and in truth" (Jn. 4:24). Physical location is no more important for worship, but rather our spiritual "location" is important. We are to worship "in spirit," and therefore we are to worship God in the Holy Spirit, discerning spiritual things. We are to worship God "in truth," and thus we are to worship God truthfully, not entertaining false notions of who He is or what He has done.
We are to worship God truly. Thus, the first commandment tells us not to have any false gods (Ex. 20:3, Deut. 5:7). But we are to also worship God in a true manner, therefore we have the second commandment (Ex. 20:4-6, Deut. 5:8-10). To worship the true God in a false manner is sin. When the Israelites fashioned the Golden Calf, they were not worshiping a false god but worshiping YHWH falsely in the form of the idol of the golden calf. We see this in the people stating that the Golden Calf represents the God who brought them out of Egypt and Aaron proclaiming a feat to YHWH (Ex. 32:4-5), indicating that the people did not see themselves as worshiping a false god but rather worshiping the true God, albeit in the manner of the pagans. God of course was not amused, and severely judged Israel. In God's eyes, worshiping Him in a false manner is no different from worshiping an idol, and therefore the Golden Calf was treated as idolatry.
Cain and Abel
The episode of Cain and Abel is significant because here both brothers made an offering to God, but God accepted Abel's offering while rejecting Cain's offering (Gen. 4:4). We are not told specifically why God rejected Cain's offering while accepting Abel's offering. We are told that Abel offered a more acceptable sacrifice (Heb. 11:4), and that Cain's deeds were evil (1 Jn. 3:12), yet even in 1 John 3:12 it could be the case that the evil deed of Cain pertains to the sacrifice not that he was, initially, morally wicked.
From the explicit teaching of Scripture, we can only say that Cain's offering was somehow deficient. But since we believe that elements of the Mosaic law did not originate from Moses but were present even from creation, it is conceivable that Cain's sacrifice was deficient because it was the wrong sacrifice, a grain offering rather than a sin offering. (There is no indication that Cain's offering was inferior to Abel's since they were both valued equally, c.f. "also" in Gen. 4:4). In other words, Cain worshiped God not in the way He was shown to do so, through the shedding of blood (c.f. Gen. 3:21)