What is the origin of blackbody radiation? Of course I know what black-body radiation is, like everyone else who has taken a thermal or statistical physics course. But it was recently pointed out to me that one thing that is rarely taught (including to me) is what the mechanism for the radiation is.
At the particle level, how does black-body radiation arise (which radiative process is this)? In other words, where are the photons coming from?

To perhaps clarify a bit further, borrowing a comment from Kevin Driscoll on an answer:

The point of the question is that there are materials whose emission spectra are quite well described by a black-body spectrum. And yet we know that at the atomic level photon emission are caused by some quantum mechanical transitions. So, how is it that such an underlying quantum mechanical description gives rise to a black-body spectrum at everyday temperatures? What is the mechanics that causes light to be absorbed/emitted at all frequencies rather than at the discrete set we might expect from the electronic transitions in isolated atoms?

With a caveat from me:

That's a good re-statement, though I'd caution that the description need not a priori be quantum mechanical in nature - there is radiation in classical electrodynamics.

 A: That information is not contained within the bb radiation - all that can be gleaned is an emitting area and a temperature.
In practice the radiation can have arisen from any process where it is feasible for a photon at that frequency to be produced.
Of course to actually be a blackbody emitter there must also be a 100% chance that a photon at that frequency incident on the object is absorbed. This condition ensures that there are relevant radiative processes that are capable of emitting at that frequency too, since there are straightforward proportionalities (for instance) between the Einstein coefficients for absorption and both stimulated and spontaneous emission (the same is true of continuum processes too).
To perhaps over-elaborate, if you postulated a hypothetical object that is incapable of emitting light at some frequencies (e.g. a two-level atom with an Einstein spontaneous emission A coefficient approximating a delta function in frequency), you might never be able to make it thick enough to absorb at those frequencies and it couldn't be a blackbody. However, even for such a system there is a tiny chance of absorption at all frequencies, due to natural or doppler broadening. If you did make the material optically thick at all frequencies (ie physically very, very thick) then its output would still approximate a blackbody.
Therefore, if you wanted to answer probabilistically, then I would say that the most likely relevant emission process will be the inverse of whatever absorption process makes the blackbody object optically thick at that frequency.
So for example, the visible (almost) blackbody radiation from the Sun's photosphere you obviously have all the optical atomic and ionic (a few molecular) transitions, but also free-free and free-bound emission corresponding to the opacity contributed by ions (mainly H$^{-}$, the dominant opacity source in the photosphere).
