RegionPlot3D in cylindrical or spherical coordinates?

You can always hide away the coordinate transformations inside a function that calls RegionPlot3D. Here's a quick & dirty sphericalRegionPlot3D:

sphericalRegionPlot3D[
  ineq_, {r_, rmin_: 0, rmax_: 1}, {th_, thmin_: 0, thmax_}, {ph_, 
   phmin_, phmax_}, opts___] := RegionPlot3D[With[{
     r = Sqrt[x^2 + y^2 + z^2],
     th = ArcCos[z/Sqrt[x^2 + y^2 + z^2]],
     ph = ArcTan[x, y] + Pi},
    ineq && rmin <= r <= rmax && thmin <= th <= thmax && 
     phmin <= ph <= phmax],
   {x, -rmax, rmax}, {y, -rmax, rmax}, {z, -rmax, rmax},
   MeshFunctions -> {Sqrt[#1^2 + #2^2 + #3^2] &, ArcTan[#1, #2] &, 
     ArcCos[#3/Sqrt[#1^2 + #2^2 + #3^2]] &}, opts];

SetAttributes[sphericalRegionPlot3D, HoldAll];

Example:

sphericalRegionPlot3D[
 Mod[ph, Pi/3] < Pi/6, {r, 2, 3}, {th, 1, Pi}, {ph, 0, 2 Pi}, 
 PlotPoints -> 100, Mesh -> {3, 60, 30}]

While not positive, I believe the answer is that RegionPlot does not support spherical (or other non-Cartesian) coordinates natively.

If correct, I guess the question becomes "What's the easiest way to plot a region defined in terms of spherical coordinates, without resorting to converting the equations by hand?" V9 has commands to ease this process.

Here are a couple of examples that show how you can use the TransformedField field command to convert your expression and you can use CoordinateTransform to generate a mesh that reflects the coordinate system that you want.

sphericalExpression = 1 + rho^2 - 2 rho*Cos[theta] Sin[phi];
cartesianExpression = 
 TransformedField["Spherical" -> "Cartesian", 
  sphericalExpression, {rho, phi, theta} -> {x, y, z}]
meshFunctions = Function /@ CoordinateTransform[
   "Cartesian" -> "Spherical", {#1, #2, #3}]
RegionPlot3D[cartesianExpression < 1, {x, 0, 2}, {y, -1, 1}, {z, -1, 1}, 
 MeshFunctions -> meshFunctions, PlotPoints -> 50, MaxRecursion -> 8,
  ViewPoint -> {2, 0, 3}, Boxed -> False, 
 AxesEdge -> {{-1, -1}, {1, -1}, {1, -1}}]

I've cranked up PlotPoints and MaxRecursion since mesh lines are fairly complicated on the other side of the figure.

Show[%, ViewPoint -> {-3, 0, 2}]

That example was chosen to yield a simple expression in Cartesian coordinates. Arbitrary expressions might yield numerical warnings but generally work. If you'd like to constrain your figure to lie within a sphere, you can do so by including a x^2+y^2+z^2<1 in your region specification.

sphericalExpression = Sin[rho] + Cos[theta]*phi;
cartesianExpression = 
 TransformedField["Spherical" -> "Cartesian", 
   sphericalExpression, {rho, phi, theta} -> {x, y, z}] // Simplify
RegionPlot3D[
  cartesianExpression < 1 && x^2 + y^2 + z^2 < 1, {x, -1, 1}, {y, -1, 
   1}, {z, -1, 1}, MaxRecursion -> 5, PlotPoints -> 50,
  MeshFunctions -> meshFunctions] // Quiet

More generalized version:

 newRegionPlot3D[
   expr_, {u_, umin_, umax_}, {v_, vmin_, vmax_}, {w_, wmin_, wmax_}, tr_, opts___] := 
 Module[{x, y, z, newExpr, xyz}, 
  newExpr = TransformedField[tr -> "Cartesian", expr, {u, v, w} -> {x, y, z}];
  xyz = CoordinateTransform[tr -> "Cartesian", {u, v, w}];
  {xmax, ymax, zmax} = NMaxValue[{#, 
       umin < u < umax && vmin < v < vmax && wmin < w < wmax}, {u, v, w}] & /@ xyz;
  {xmin, ymin, zmin} = NMinValue[{#, umin < u < umax && vmin < v < vmax && wmin < w < wmax}, {u, v, w}] & /@ xyz;
  RegionPlot3D[
   newExpr, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}, opts]
]

Some examples:

newRegionPlot3D[r < 1, {r, 0, 1}, {phi, 0, 2 Pi}, {th, 0, Pi}, "Spherical"]
newRegionPlot3D[ro < 1, {ro, 0, 1}, {phi, 0, 2 Pi}, {z, 0, 1}, "Cylindrical"]