uses ShellApi
...
private
procedure WMDROPFILES(var Message: TWMDROPFILES);
message WM_DROPFILES;
{ Private declarations }
...
procedure TForm1.WMDROPFILES(var Message: TWMDROPFILES);
var
NumFiles : longint;
i : longint;
buffer : array[0..255] of char;
begin
{How many files are being dropped}
NumFiles := DragQueryFile(Message.Drop,
-1,
nil,
0);
{Accept the dropped files}
for i := 0 to (NumFiles - 1) do begin
DragQueryFile(Message.Drop,
i,
@buffer,
sizeof(buffer));
Form1.Memo1.Lines.Add(buffer);
end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
DragAcceptFiles(Form1.Handle, True);
end;