the get_Item method of the Rows collection will throw that exception if the specified rowIndex is less than zero. Add a check to ensure that the handler will not try to access the Rows collection if the rowIndex is invalid. Also, I would add a check to ensure that the Value property of the selected cell is not null.

private void main_ListDataGridView_CellClick(object sender, DataGridViewCellEventArgs e)
{
    if(e.RowIndex >= 0 && main_ListDataGridView.Rows[e.RowIndex].Cells[e.ColumnIndex].Value != null)
        Clipboard.SetText(main_ListDataGridView.Rows[e.RowIndex].Cells[e.ColumnIndex].Value.ToString());
}