The Monge Patch

ParametricPlot3D[{u, v, u^2 + v^2}, {u, -3, 3}, {v, -3, 3}]

ParametricPlot3D[{{u, v, u^2 + v^2}, {u, v, -1}}, {u, -3, 3}, {
        v, -3, 3}]

Surface of Revolution

ParametricPlot[{u, (Cos[u^2] + 2)/(u + 1)}, {u, 0, 4}]

ParametricPlot3D[{u, (Cos[u^2] + 2)/(u +  1) Cos[v],  
        (Cos[u^2] + 2)/(u + 1) Sin[v]}, {u, 0, 4}, {v, 0, 2 Pi}]

ParametricPlot3D[{u, (Cos[u^2])/(u +  1) Cos[v],  
        (Cos[u^2])/(u + 1) Sin[v]}, {u, 0, 4}, {v, 0, 2 Pi}]

The "Cone"

ParametricPlot3D[{10, 10, 10} + v {2 Cos[u],  2 Sin[u],  4}, {u, 
        0, 2 Pi}, {v, 0, 20}]

ParametricPlot3D[{10, 10, 10} + v {2 Cos[u],  2 Sin[u],  4}, {u, 
        0, 2 Pi}, {v, -10, 20}]

ParametricPlot3D[{10, 10, 10} + v {2 Cos[u],  2 Sin[u],  4}, {u, 
        Pi/2,   7/4 Pi}, {v, -10, 20}]

The "Cylinder"

ParametricPlot3D[{4 Cos[u],  4 Sin[u],  1}  +  v {10, 10, 10}, {
        u, 0, 2 Pi}, {v, 0, 1}]