Автор: http://www.swissdelphicenter.ch

uses
  registry;

function IE_installed(var Version: string): Boolean;
var
  Reg: TRegistry;
begin
  Reg := TRegistry.Create;
  with Reg do
  begin
    RootKey := HKEY_LOCAL_MACHINE;
    OpenKey('Software\Microsoft\Internet Explorer', False);
    if ValueExists('Version') then
      Version := ReadString('Version')
    else
      Version := '';
    CloseKey;
    Free;
  end;
  Result := Version <> '';
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  IE_Version: string;
begin
  if IE_Installed(IE_Version) then
    ShowMessage(Format('Internet Explorer %s installed.', [IE_Version]));
end;