In the original P&P model, we had a nice story in which there was supposed to be some finite list of principles and some finite list of parameters, the former constraining hypotheses and the latter driving what kinds of things kids should be looking for. So, wh-islands and Binding theory are principles, and head-directionality parameter and wh-in-situ vs. wh-movement examples of parameters.
However, I think in the theoretical literature (specifically in Minimalism, and earlier in other lexicalist approaches) the "toolkit" model of variation has more or less become the standard -- UG provides the tools and format for creating languages, and there are any number of ways they can be used. There is a theory of variation, the "Chomsky-Borer Conjecture" (Borer 1984, Chomsky 1995) in which the variation between languages is restricted to what functional elements look like, which can be thought to be a flavor of this.
However, I'm wondering what people think from the acquisition side of things. The idea that languages could vary in any number of ways consistent with principles – and parameters provide no delineation – basically says that we can't really learn anything about acquisition from typology, and that every aspect of variation is something the child has to learn ex nihilo.
Do kids usually assume that their language will be typologically "unmarked" until they receive evidence to the contrary? To kids seem to lump together properties (do head-final kids like scrambling more often than head-initial kids?) Is the notion of "parameter" still useful in generative approaches to language acquisition?