In general the Poynting vector is the in the direction in which the wave propagates. Usually, for university level work etc, for the most part we already know the direction of the EM wave. Thus the Poynting vector comes out positive, and in the direction we have predefined. However, if, for instance, we rotate our coordinates, the Poynting vector will point in the direction of propagation in the new coordinate system.
Now the direction of propagation can for instance be in the direction of the negative z axis, which would yield a 'negative' vector.
Having said that, if by 'negative' one means that the amplitude is negative, i.e. the energy propagation is negative, this would imply the 'source' of the wave is actually gaining energy as opposed to radiating it. This is possible for instance when you have an antenna that receives radiation. What is meant by that is that the external wave is oscillating the charge in the antenna, thus deposits energy into the antenna.
In that case though you need to take the viewpoint of the charge at the antenna to get the so-called negative Poynting vector.