Просто используйте: dataGridView1.CurrentCell.Value.ToString()
private void dataGridView1_MouseDoubleClick(object sender, MouseEventArgs e)
{
MessageBox.Show(dataGridView1.CurrentCell.Value.ToString());
}
или
// dataGrid1.Rows[yourRowIndex ].Cells[yourColumnIndex].Value.ToString()
//Example1:yourRowIndex=dataGridView1.CurrentRow.Index (from selectedRow );
dataGrid1.Rows[dataGridView1.CurrentRow.Index].Cells[2].Value.ToString()
//Example2:yourRowIndex=3,yourColumnIndex=2 (select by programmatically )
dataGrid1.Rows[3].Cells[2].Value.ToString()