Yes I am a theonomist. No I am not a theonomist. Both equally true. Strange, yes? Yes.
Above is my postmodern answer. Below is a coherent, understandable answer. (I'm in a bit of a goofy mood today).
When most people think of theonomists they think of R.J. Rushdoony or Gary North, who, understandably have been the figureheads of the movement. However, Greg Bahnsen once said, in Theonomy in Christian Ethics, that not all theonomists agree on how to apply God's law to society or even to 'individual' morality. This, I think, is what needs to be the first thing people hear about theonomy: it isn't a monolithic movement.
What is a theonomist? A theonomist is someone who says that God's law (as revealed especially in the Torah, but expanded and conditioned by revelation and history--particularly Jesus' history) is still applicable to all of life's relationships, unless specifically changed by the teachings of Jesus or his apostles/disciples in the Biblical canon. This usually boils down to a question of how God's law applies to the 'State' (or at least people take it in that direction very fast).
After that, though, theonomists are a mixed bunch. Some say that the mixed fabric laws are still in force, others that all the 'separation' laws are fulfilled and abrogated in Christ. Some say that stoning is the only acceptable method of the death penalty, others that the death penalty is fulfilled in Christ. Some say that the State should have limited powers, others that there should be no State. Quite a broad range, eh?
Having read Institutes of Biblical Law: Vol. 1 this summer, I got a new view of theonomy. Rushdoony spent many pages talking about lawful land use that could very well have come from the same pen as Wendell Berry uses. That was a shock to me, since many theonomists think that Berry is a 'liberal'.
What use should the Torah have today? I think it should have a lot--since God doesn't author things that are of little to no use. Yes, they must be brought into new historical circumstances (but so does the rest of Scripture). It must also be thought through very carefully. The governmental regulations in, say, Exodus 18 and even Deuteronomy 17, would only really work in a faithful, mostly agraian society (maybe that's why I like theonomy so much!). It advocates smaller communities based on the love engendered by the Exodus (mercy to widows, orphans, and strangers), but still has the needed discipline to keep 'justice' (a tricky word to define without the Torah as a backdrop).
Since the Torah is essentially storied, I think that it needs to be rethought with the developments of the story. What was God saying to the beleaguered Exodus community with the separation laws? Is it something similar to what non-theonomists Walsh and Keesmaat say in their chapter "An Ethic of Secession" from Colossians Remixed? I would be inclined to say yes. Are there things in Torah that should only be symbolically fulfilled since the Messiah? Yes again--the priestly regulations would fall under here. Can the Torah be used in anti-creational, anti-merciful ways? Yes, like in all eras from its Sinai giving to today. Redemption itself (which many use to say 'freedom from God's law') is an Exodus metaphor, which implies (at least) that God gives his law in covenant renewal--such as Jesus' reclamation of the law in Matthew 5.
A complete picture? No. Things to think about? Yes.
PS--Are there anarchistic, non-ecclesiastical theonomists? You bet your booty. Read especially "The Christmas Conspiracy" where I was first introduced to what I recognize as incredibly similar to many neocalvinist writings.