We introduce two classes of spatial optical breathers in strongly nonlocal nonlinear media: multiringed breathers and rotating breathers, which can be created as results of the superposition of off-waist input Laguerre-Gaussian beams. Their width ``breathes'' sinusoidally during propagation under the off-waist incident condition, whatever the input power is. Only when the beam is inputted at the waist and the input power equals the critical power simultaneously would the multiringed (rotating) breather reduce to a multiringed (rotating) soliton. For a rotating breather, the azimuthal orientation of the intensity pattern is determined by the indices of the constituent beams and varies periodically in propagation. This property together with the breath of the beam width yields novel trajectories which the points within the beam cross section undergo.