Screen to World Coordinates

[User137]

You didn't mention what you are trying to do, but when it comes to getting screen to world coordinates on various 3D objects or just 2D plane, this is what i do:
1) Calculate mouse-ray that goes from mouse towards infinity. (You only need to do this once per frame tick)
2) Calculate its collision point with a plane. Or calculate with each face of a 3D model.
Good thing is that in the process you get information such as face normal in collision point and which face it hits.

Then some code from Next3D:

procedure TNXGL.GetMouseRay(const mx, my: single; const p, normal: PVector;
  rayMove: single);
var viewport: TGLVectori4;
    modelM,projM: TGLMatrixd4;
    x1,y1,z1,x2,y2,z2: double;
    n: TVector;
begin
  glGetIntegerv(GL_VIEWPORT,@viewPort);
  glGetDoublev(GL_PROJECTION_MATRIX,@projM);
  glGetDoublev(GL_MODELVIEW_MATRIX,@modelM);
  {$HINTS OFF} // hints about x1..z2 not initialized
  gluUnProject(mx,my,modelM[2,3],modelM,projM,viewport,x1,y1,z1);
  gluUnProject(mx,my,modelM[2,3]-1,modelM,projM,viewport,x2,y2,z2);
  {$HINTS ON}
  n.x:=x1-x2; n.y:=y1-y2; n.z:=z1-z2; n:=Norm(n);
  if p<>nil then begin
    p^.x:=x1+n.x*rayMove;
    p^.y:=y1+n.y*rayMove;
    p^.z:=z1+n.z*rayMove;
  end;
  if normal<>nil then normal^:=n;
end;

// Result >= 0 if intersection happens
function RayPlaneIntersect(const rayOrigin, rayDirection,
  planeOrigin, planeNormal: TVector; intersection: PVector): single;
var d,numer,denom: single;
begin
  d:=planeNormal.x*planeOrigin.x+planeNormal.y*planeOrigin.y+planeNormal.z*planeOrigin.z;
  numer:=-planeNormal.x*rayOrigin.x-planeNormal.y*rayOrigin.y-planeNormal.z*rayOrigin.z+d;
  denom:=planeNormal.x*rayDirection.x+planeNormal.y*rayDirection.y+planeNormal.z*rayDirection.z;
  if denom=0 then begin
    result:=-1; exit;
  end;
  result:=numer/denom;
  if intersection<>nil then begin
    intersection^.x:=rayOrigin.x+result*rayDirection.x;
    intersection^.y:=rayOrigin.y+result*rayDirection.y;
    intersection^.z:=rayOrigin.z+result*rayDirection.z;
  end;
end;

function TNXGL.MouseRayAtPlane(const mx,my: single; const planePos,planeNormal: TVector): TVector;
var rayOrigin, rayDirection: TVector;
begin
  GetMouseRay(mx,my,@rayOrigin,@rayDirection);
  rayPlaneIntersect(rayOrigin,rayDirection,planePos,planeNormal,@result);
end;