(* Ellipsoid *)
ContourPlot3D[x^2/9+y^2/4+z^2==1,{x,-3,3},{y,-3,3},{z,-3,3}]

(* Hyperboloid (one sheet) *)
ContourPlot3D[x^2/2+y^2==z^2/3+1,{x,-3,3},{y,-3,3},{z,-3,3}]

(* Hyperboloid (two sheets) *)
ContourPlot3D[x^2/2+y^2==z^2/2-1,{x,-3,3},{y,-3,3},{z,-3,3}]

(* Paraboloid (elliptic) *)
ContourPlot3D[x^2/2+y^2==z,{x,-3,3},{y,-3,3},{z,-3,3}]

(* Paraboloid (hyperbolic) *)
ContourPlot3D[x^2/2-y^2==z,{x,-3,3},{y,-3,3},{z,-3,3}]

(* Cone (elliptic) *)
ContourPlot3D[x^2/2+y^2==z^2/3,{x,-3,3},{y,-3,3},{z,-3,3}]