There has been continual concern from a variety of believers worldwide about certain modern worship practices and whether they are valid expressions of worship in a Biblical sense. As one who stays aloof from such things, I do not find this controversy particularly, er, stimulating (grin) but hope to be able to shed some objective light on the subject by taking a look at how worship was performed in the Bible and allowing readers to draw their own conclusions.
Our sources for this study are A. H. Herbert's Worship in Ancient Israel; Worship in the Hebrew Bible [WAHB], a collection of essays edited by Graham (no, not Billy!), Marrs (no, not Texe!) and McKenzie; and Edwin Yamauchi's article, "Old Testament Exegesis on the Hebrew Terms for Prostration and Worship." We also have thoughts from Torrance's Worship, Community and the Triune God of Grace and Peterson's Engaging with God. The latter is an especially useful text and we would recommend it for serious students of this subject.
Why was worship performed? Herbert [5, 8] notes that worship was a human reaction to awareness of the characteristics of God: holiness, righteousness, justice, mercy. The reaction was always expressed in the presence of God, but God's presence was not required for it to be enacted. It was also a reaction to God's salvific acts in history .
Today we speak of "proper object" of worship and this is not so controversial beyond alternative faiths (Unitarians, etc.).
What constituted worship? This is where the meat hits the fan -- what some speak of "proper practice". On this we have ideas ranging from charismatic expressions to the Church of Christ banning musical instruments.
Herbert and Yamauchi both offer studies of the vocabulary of worship in the OT. The first main word, usually translated as "to worship" is shachah. As Herbert notes, this word "emphasizes the physical expression appropriate before a leader or a king." It is used in the Bible this way, to refer to prostration before leaders, and the equivalent word in Canaanite language is used "by the vassal kings of Canaan as they acknowledge the sovereignty of the Pharaoh." Yamauchi writes:
Prostration was quite common as an act of submission before a superior. Vassals in the Amarna letters write, "At the feet of the king ... seven times, seven times I fall, forwards and backwards." (Cf. ANEP, fig. 5.) Jehu or his servant bows down on his knees with his forehead touching the ground before Shalmaneser III on the Black Obelisk (cf. ANEP, fig. 351).
Oddly enough, Yamauchi notes that this word is used less frequently of men's acts before God than it is used of men's acts before other men (kings, etc.). Yamauchi also notes one clear example of the word used to refer to a physical act without devotion:
In an interesting passage the verb is used both of "worship" and of "bowing" without an attitude of worship. After Naaman's healing and his conversion to the monotheistic worship of the Lord (II Kgs 5:17), the Syrian officer asked Elisha, "In this matter may the Lord pardon your servant: when my master (i.e. the king) goes into the house of Rimmon to worship there, leaning on my arm, and I bow myself in the house of Rimmon, when I bow myself in the house of Rimmon, the Lord pardon your servant in this matter" (II Kgs 5:18, RSV). Elisha did not object and said, "Go in peace."
Defined thusly, "worship" is not a unique religious act, but an act of submission. Emphasis of course should not be placed on the physical act, for as the Namaan example shows, one can "worship" in insincerity. This is sensible under the rubric of the Semitic Totality Concept the body, in worship, merely follows what the intangible part of ourselves thinks. In this light we see as well the intimate connection between worship and ethics in the OT -- as is sensible, one in submission to God will act as God wants them to.
Worship thus becomes in a real sense (as defined here) an act that is continual [Marrs, WAHB, 203]. Roberts [WAHB, 269f] draws and eerie parallel to the modern American church and the Jews in Isaiah's day (1:15-17) that apparently "went to church" but whose worship was "found unacceptable because the rest of Israel's life was characterized by sin, oppression, and injustice."
Peterson [184-5] notes for comparison that Paul, for example, in Philippians 2:17 referred to himself in his service as a "libation" or offering like an OT sacrificial offering. His actions and life as a whole were compared to an act of worship. As Peterson sums it up: "...expressions of faith in the saving work of Jesus Christ and ministries that encourage such faith are specifically the worship acceptable and pleasing to God in the gospel era."  Worship means serving God "in a whole range of relationships and responsibilities."
Then there is a term used in worship, not much at all (only twice), but not meaning "worship" by the direct definition: hilluwl. Herbert notes that this word "draws attention to the fact that Israel's worship was distinctly vocal in character; it is to shout exultantly." It is here where some of us may center our arguments: Are we not to do the same? I would say it is not required, but is allowed.
"Praise" is depicted by example but is mentioned in the "practice handbook" material in the Torah only at Lev. 19:24: "But in the fourth year all the fruit thereof shall be holy to praise the LORD withal."
Another word for "praise" is yadah. This word seems nearly synonymous with shachah, Here's one more: barak.
In these words we seem to have the combination of physical prostration and verbal expression. Does it need to be "loud" as some suppose? I would suggest that it can be, but need not be. As noted in works like Our Father Abraham, these practices reflect the character of the Hebrew mindset. Thus Allen in WAHB  notes that there exists in worship passages in Ezra and Nehemiah a "tension of ardent lament and exuberant joy." One may consider by comparison the "hot and cold" attitudes and language of the Hebrews (see here).
I do not see here any "requirement" for the staid modern to copy the practices exactly and to the same "volume" as the Hebrews. If anything I would advise a modern reader to be cautious in trying to imitate them against one's own ingrained psychological matrix.
Herbert goes on to describe the media of worship in ancient Israel, which included sacrifices, ritual recitals, and cultic objects like the Ark. He concludes that worship must include "recognized public acts and words through which the approach to God is made, and recognized media through which and whom God is known to approach His people."  These media of course were not regarded as transcendentally permanent; verses like Jer. 7:22 and the analysis of Hebrews that sacrifice is not adequate, show that the "fulfillment of Israel's worship could only come, as the Old Testament fully realizes, from God's side; and it must be in a higher category than that of animal and Temple." As has been often said, motives rather than practice seem to be the key.
Graham in WAHB  after a study of 2 Chron. 30-31 sums up the matter by concluding that the text's "theology of worship suggests a certain balance and flexibility, all maintained and articulated in the devoted service of God." Graham rightly observes that popular culture today has shifted focus in worship from God to self; from what God is to "what God can do for me". Torrance  retells for comparison the person who reacted to a beautiful valley view by remarking that by using a dam to flood the valley, enough water could be provided to irrigate nearby farms.
Thus worship becomes self-centered rather than community-oriented; need becomes the preoccupation; joy and praise push out remorse for sin and lament, and we are as far from the Hebrew original as we can be, having emasculated what we do not like. Worship is "a time for reorientation of the human heart--to remember what God has done in the past and to infuse the present with hope for a future life of well-being and communion with God." Knowledge of God is essential for worship; the focus needs to be on WHO God is, not What God does for US -- which makes today's evangelism tactic of "personal testimony" a case of imposing modern self-centered values.
Roberts adds  after a study of worship in Isaiah: "The trend to simplify worship -- by removing theological complexity, to make it more popular by emphasizing entertainment at the expense of education and to increase its appeal by stressing religious experience -- has little in common with the ideal of worship envision by Isaiah." As he wryly adds, "Isaiah does not appear to have been entertained by the worship service in which he experienced his vision of God, and, at least in the short run, it does not seem to have made him feel better about himself or his neighbors". As Torrance notes, one may as well say that one gets married for the purpose of having someone around to cook, clean house, or fix the plumbing. 
In conclusion: "Worship" is often used to refer just to the time of singing and music in our services, but it is clear from contextual study that worship is a life and lifestyle, not just acts in isolated pockets of time. Worship can mean serving in a soup kitchen, or going on a mission trip, or conducting a ministry of some sort -- and we may consider deeply how far our Western, individualistic perceptions have in some cases taken us from the NT ideal.