Nathan Busenitz provides at http://www.sfpulpit.com a helpful summary of the various positions to the issue:
(1) that New Testament believers are not under the Mosaic Law; and (2) that at the same time the New Testament authors esteem and appeal to that same Mosaic Law.
David Dorsey (in “The Law of Moses and the Christian: A Compromise,” JETS 34/3 (Sept. 1991): 323–24) summarizes six of these positions:
He also includes the Ten Commandments before Moses, under Moses, and After Moses:
1. Marcion. This second-century heretic’s gnosticism led him to view the strict and harsh God of the OT as different from and inferior to the “good God” revealed by Christ in the NT. Consequently Marcion jettisoned the entire OT—with its “Jewish” law—from his canon. . . .
2. Dispensationalism. This hermeneutical approach holds that God has developed different programs for his people in different ages and that the particulars—including the laws—that belong to the “dispensation of law” (Exodus 20—Malachi) are not binding upon God’s people in this present “dispensation of grace.” . . .
3. Covenant theology. . . . Reformed theologians see a greater continuity between the Testaments, maintaining that … there are not two covenants but one, and Christians are part of that covenant. We live under the “renewed” covenant, not the “new” covenant. The Church is spiritual Israel, and the laws of the Mosaic covenant are accordingly our laws [although often spiritualized]. . . .
4. Seventh-Day Adventism. Adventists . . . protest that it is inconsistent to accept the Ten Commandments as normative for all times and then reject or modify the fourth commandment. The entire Decalogue, including the injunction to observe the seventh day, is binding upon all Christians. [They also observe some dietary laws.] . . .
5. Christian reconstructionism. Also called theonomy or the Chalcedon school, this recent spinoff from Reformed theology argues for the normativity of not only the moral laws but also the civic regulations. . . .
6. World-Wide Church of God. . . . Herbert W. Armstrong argues that only a few of the laws, such as the sacrificial regulations, are no longer valid because they have been fulfilled in Christ, and that the great majority of laws still apply to spiritual Israel, including the Ten Commandments, with the observance of the seventh day, the keeping of all the Jewish feast days and holy days, the observing of the dietary laws, and some of the ceremonial laws.
1) First Commandment (Polytheism) – Gen. 35:2; Ex. 20:3; 1 Thess. 1:9
2) Second Commandment (Graven Images) – Gen. 31:39; Ex. 20:4; 1 John 5:21
3) Third Commandment (Swearing) – Gen. 24:3; Ex. 20:7; cf. James 5:12
4) Fourth Commandment (Sabbath) – Gen. 2:3; Ex. 20:8; Col. 2:16; cf. Heb. 4
5) Fifth Commandment (Obey Parents) – Gen. 27:41; Ex. 20:12; Eph. 6:1
6) Sixth Commandment (Murder) – Gen. 4:9; Ex. 20:13; 1 John 3:15
7) Seventh Commandment (Adultery) – Gen. 39:9; Ex. 20:14; 1 Cor. 6:9, 10
8) Eighth Commandment (Theft) – Gen. 44:4–7; Ex. 20:15; Eph. 4:28
9) Ninth Commandment (False Witness) – Gen. 39:17; Ex. 20:16; Col. 3:9, 10
10) Tenth Commandment (Coveting) – Gen. 12:18; 20:3; Ex. 20:17; Eph. 5:3
(This list was adapted from The MacArthur Study Bible, 124 and Walt Kaiser, Toward OT Ethics, 81-82)