What are all the fields that we know so far that can be associated to charges of the kind "+" and "-" (not necessarily the electric +/- charges). I already know the EM field. Are there other examples? Will the disturbances in such a field propagate slower than the speed of light? (like for the EM field)
Example: not gravity because we haven't found anti-gravity (or "negative mass" particles that climb the gravitational field in the opposite direction).
I think pretty much any problem that is formulated as a continuity equation with a non-zero "source" term can be described in similar terms. In differential form the continuity equation is $$\frac{\partial\rho}{\partial t}+\vec\nabla\cdot\vec J = g$$ where $\rho$ is the spatial density of a quantity that is conserved in some sense (think number of particles per unit volume), $\vec J$ is the flow rate or "flux" of this quantity (particle current density, i.e. flow per unit time per unit area), and $g$ is the rate at which this quantity is generated or "sourced" per unit volume (how fast particles are created). To see how this fits with electrostatics, compare with Gauss' law: $$\vec\nabla\cdot\vec D = \rho.$$ We see that charge density "sources" the E-field, which serves as the "flow rate".
The classic analogy for electrostatics is the flow of an incompressible fluid that fills all space. In this analogy, charge ($\text C$) becomes the rate at which fluid is sourced into (positive) or sinked out of (negative) the space ($\text{kg/s}$), $\vec E$ ($\text{V/m}$) becomes fluid velocity ($\text{m/s}$), and $\epsilon$ ($\text{F/m}$) becomes the fluid density ($\text{kg/m}^3$). There are lots of other examples, here are just a few:
If you are looking for "charges" that are conserved (i.e. the amount of total charge is constant), see the examples listed here, along with Noether's theorem.
