This thread goes way back, but if someone new stumbles upon this situation this might help:
In addition to what 'adocas' said, which was not working for me because of conversion between DataGridRow & DataRow not working, I came up this solution:
private void yourDataGrid_MouseDoubleClick(object sender, MouseButtonEventArgs e)
{
foreach (DataRowView row in yourDataGrid.SelectedItems)
{
System.Data.DataRow MyRow = row.Row;
string value = MyRow["columnname" (or index)].ToString();
}
}