data = Flatten[Table[
  {x, y, PDF[MultinormalDistribution[{0, 0}, {{0.2, 0.1}, {0.1, 0.4}}],{x, y}]},
  {x, -2, 2, 0.01}, {y, -2, 2, 0.25}],1];

gb = GatherBy[data, #[[2]] &];

cLines = Transpose[{
  ColorData["BlueGreenYellow"] /@ Rescale[Range[Length[gb]]],
  Line /@ gb
}];

Graphics3D[
 {Thick, cLines},
 Axes -> True, Boxed -> False, BoxRatios -> {1, 1, 1},
 FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}},
 AxesLabel -> {"x", "y", "z"}, PlotRangePadding -> None]

f[x_, y_] := Exp[-x^2 - y^2/(4 + x^2/4) + x y];
ParametricPlot3D[Table[{x, y, f[x, y]}, {y, -5, 5}], {x, -5, 5},
                 PlotRange -> All]