Owh, forgot about the TCheckListBox. That goes exactly the same:
procedure TForm1.Button2Click(Sender: TObject);
var
I: Integer;
begin
Memo1.Clear;
for I := 0 to pred(CheckListBox1.Items.Count) do begin
if CheckListBox1.Checked[I] then Memo1.Lines.Add(CheckListBox1.Items[I]);
end;
end;