How high are cyclones, normally?

If, by cyclone, you mean tropical cyclone (such as Tropical Cyclone "Yasi", or Tropical Cyclone "Carlos") then the clouds of the eye wall and the thunderstorms in the spiral bands go all the way to the tropopause, the boundary between the troposphere and the stratosphere. In the tropics, where these systems develop, the tropopause is around 15.5km up (50,000ft or so), so the cyclone will be that high.