Conduction, convection, radiation: Does evaporation count as one of those? The forms of heat transfer are traditionally described as conduction, convection, and radiation.  Is evaporation (or any other change of state) counted as one of those forms?  Or is it considered its own distinct form of heat transfer?
 A: In engineering, heat transfer covers various mechanisms, including thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes (e.g. evaporation).
At a given pressure, different boiling regimes exist depending on temperature (the following image applies to water at a pressure of 1 atm).

Image source: Wikipedia
In particular, the nucleate boiling regime is important in engineering (e.g. for the design of nuclear reactors) because of the high heat flux at small temperature differences. In this regime, isolated steam bubbles form at the hot surface, separate from the hot surface, and may condense again somewhere else in the subcooled liquid. Thus, in addition to the heat transfer by convection, the steam bubbles carry away heat in form of their enthalpy of vaporization $\Delta H_\mathrm{vap}$ which is released again when the bubbles condense. Furthermore, the movement of steam bubbles increases the movement of the liquid, thus increasing the heat transfer by convection.
(Note that if too much steam is generated at the hot surface, the steam insulates the hot surface from the liquid, thus strongly decreasing the heat flux after reaching the critical heat flux.)
A: Evaporation appears equivalent to one of the cases of heat being transported because the vapor carries enthalpy content away from the liquid. In this regard, one might also claim that fusion (melting) is type of heat transfer because it also transports enthalpy, in this case from a solid by a liquid. The same could be said for sublimation (enthalpy is carried away from a solid by a vapor).
While the three process carry away enthalpy, they are not a different form of heat transfer. Heat transfer is solely the movement of heat. It is not the movement of enthalpy. The movement of enthalpy requires the movement of mass. Heat transfer excludes the movement of energy due to the movement of mass.
To illustrate further, consider the classic case of a system and its surroundings separated by a boundary. The integral form of the energy balance equation around a control volume is written as below.
$$ \iint_{CS}\ \rho \left(\tilde{e} + \frac{p}{\rho} \right) \vec{v}\bullet\vec{n}\  dA + \frac{\partial}{\partial t} \iiint_{CV}\ \rho\ \tilde{e}\ dV = \dot{q} - \dot{w}$$
On the left side, the first term is the flow of energy by mass over the control surface and the second is the time rate of change of the energy in the control volume. On the right side, the first term is the heat flow (heat transfer) into or out of the control volume and the second term is the work flow.
Evaporation moves enthalpy content through a control surface and changes the energy content in the control volume. These two effects are represented entirely on the left side. The three forms of heat transfer are encompassed in the $\dot{q}$ term.
In summary, while they carry enthalpy away from the system, the processes of vaporization, fusion, and sublimation are not different forms of heat transfer. They are phase transformations.
A: No.
Conduction, convection, and radiation refer to the transport of energy carriers, such as phonons or electrons for conduction, bulk atom/molecule flows for convection, and photons for radiation. 
These three mechanisms transport heat, while evaporation simply requires heat to occur. So evaporation may take energy away from an object, by absorbing energy of carriers such as phonons (vibrations), but it is different because it does not transport heat, unless you are speaking of the bulk convective motion of evaporated molecules afterwards.
