What are commonly used tools to reconstruct the transcriptional regulatory circuits that govern diverse cellular responses and what input data sets do they accept?
Inferring transcriptional / regulatory networks from empirical data is an active area of research, and to my knowledge there aren't many mature tools for this type of analysis. I see mostly mathematicians, statisticians, and engineers working on this problem, probably because of the intense quantitative theory involved. Even if mature tools do exist, I doubt they're tailored for the typical biologist--more likely, they are geared toward scientists with a more quantitative background.
That being said, I am aware of 2 or 3 pieces of software that may provide a starting point for the curious or the adventurous: AIRnet (described here), iBioSim (described by Barker's PhD thesis, currently the second hit on this Google search), and maybe Ingenuity Pathways Analysis (which requires a paid license). The only one of these tools I've even tried to use is iBioSim, and at the time (2 or so years ago) it was a very kludgy process.
I'd like to add regulonDB which is not as integrated, but has a tremendous map of the e coli regulome which would be useful for any bacterial model.
I agree with @DanielStandage that this is not a well understood and there don't even appear to be standard representations for this sort of data.