I wrote a post about the law and the OT ("Moses and Me") last month. Now, I'll share a few thoughts about the law and the NT believer.
1. My position is probably something of an in-between position between Lutheranism and Reformed theology. As a general point, I think the best way to understand the Law is to see it on a trajectory towards something (i.e. Christ and the life of the Spirit). It is not a final relevation of God's purposes, nor His will. It is a signpost and not a destination.
2. Further, I don't think the division of the Law into ceremonial, civil and moral is a biblical model (it is nowhere mentioned). I think we should take NT's statements about the "Law" as encompassing the whole thing, and not just bits of it.
3. I think the Law has abiding relevance for us when interpreted christologically. It has been fulfilled/completed by Christ and 'taken up' or subsumed into the "law of Christ" (e.g. Gal 6:2). Therefore, the NT believer is not ruled directly by the OT law, but by the law of Christ. On the other hand, though, the Law has great ethical relevance to the believer when looked at through Christ and read through the lens of NT ethics.
4. The Law belongs belongs to a particular administration i.e. Israel, and must be read as such. We have died (to the Law), been raised and belong to the age to come. The NT believer is in Christ and is ruled by the Spirit of God. The Spirit is his authority (as heard through Christ and the apostles) and not the Law (see pt. 2). On the other hand, the Law has relevance to the believer as a part of salvation history. It points us to Christ and our need for Him. The Law is not irrelevant and needs to be fulfilled - but it is fulfilled by Christ so that we are released into a new way of obedience.
5. The Law could never bring righteousness of life. What we need is new birth and the Spirit to live the Christian life. On the other hand, the Law itself points forward to a kind of righteousness that goes beyond it and completes it. We can learn about this righteousness by looking at it 'through the Law'.
This stuff is always controversial, so let me know what you think.