How can I generate and randomly assign color to annular sectors?

Hmm...Szabolcs beat me to it (in a comment) by one minute...

plot = ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi}, 
   Mesh -> 23, Axes -> False, 
   MeshShading -> {{Red, Green}, {Blue, Yellow}}, 
   PlotRange -> {{-9, 9}, {-4, 4}}];

plot /. poly_Polygon :> {RGBColor @@ RandomReal[1, 3], poly}

With V10 came RandomColor and ColorSpace

Using Michael E2's wonderful solution

plot =
  ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi},
   ImageSize -> 500,
   Mesh -> 13,
   MeshShading -> {{Red, Red}, {Red, Red}},
   PlotRange -> {{-9, 9}, {-4, 4}}];

Grid @ Partition[Table[plot /.
    poly_Polygon :> {RandomColor[ColorSpace -> space], poly},
         {space, {"RGB", "XYZ", "CMYK", "Grayscale"}}], 2]

Making the MeshShading setting Dynamic also works without the need for post-processing:

ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi},
 Mesh -> 23, Axes -> False,
 MeshShading -> Dynamic@{{Hue@RandomReal[], Hue@RandomReal[]},
                         {Hue@RandomReal[], Hue@RandomReal[]}}, 
 PlotRange -> {{-9, 9}, {-4, 4}}]

The same trick works in combination with V10 RandomColor:

ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi},
  Mesh -> 23, Axes -> False,BaseStyle->Opacity[.75],
  MeshShading ->Dynamic@ {{RandomColor[], RandomColor[]}, 
                        {RandomColor[], RandomColor[]}}, 
  PlotRange -> {{-9, 9}, {-4, 4}}]

ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi},
  Mesh ->{25,25}, Axes -> False, BaseStyle->Opacity[.75],
  MeshShading ->Dynamic@Evaluate@ Table[RandomColor[],{25},{2}], 
  PlotRange -> {{-9, 9}, {-4, 4}}]

ParametricPlot[r {Cos[t], Sin[t]}, {r, 0, 12}, {t, 0, 2 Pi},
  Mesh ->{25,25}, Axes -> False, BaseStyle->Opacity[.75],
  MeshShading ->Dynamic@Evaluate@ Table[RandomColor[],{2},{25}], 
  PlotRange -> {{-9, 9}, {-4, 4}}]