How to extract points from a plot

pts=Cases[theplot, x_GraphicsType:>First@x, Infinity];

Example 1:

g=Plot[Sin[x],{x,0,2Pi}];
pts=Cases[g,x_Line:>First@x,Infinity];
ListPlot[pts]

Example 2:

g=Plot3D[Cos[x]+Cos[y],{x,0,4Pi},{y,0,4Pi}];
pts=Cases[g,x_GraphicsComplex:>First@x,Infinity];
ListPointPlot3D[pts]