What is the right way to populate a DropDownList from a database?

You could bind the DropDownList to a data source (DataTable, List, DataSet, SqlDataSource, etc).

For example, if you wanted to use a DataTable:

ddlSubject.DataSource = subjectsTable;
ddlSubject.DataTextField = "SubjectNamne";
ddlSubject.DataValueField = "SubjectID";
ddlSubject.DataBind();

EDIT – More complete example

private void LoadSubjects()
{

    DataTable subjects = new DataTable();

    using (SqlConnection con = new SqlConnection(connectionString))
    {

        try
        {
            SqlDataAdapter adapter = new SqlDataAdapter("SELECT SubjectID, SubjectName FROM Students.dbo.Subjects", con);
            adapter.Fill(subjects);

            ddlSubject.DataSource = subjects;
            ddlSubject.DataTextField = "SubjectNamne";
            ddlSubject.DataValueField = "SubjectID";
            ddlSubject.DataBind();
        }
        catch (Exception ex)
        {
            // Handle the error
        }

    }

    // Add the initial item - you can add this even if the options from the
    // db were not successfully loaded
    ddlSubject.Items.Insert(0, new ListItem("<Select Subject>", "0"));

}

To set an initial value via the markup, rather than code-behind, specify the option(s) and set the AppendDataBoundItems attribute to true:

<asp:DropDownList ID="ddlSubject" runat="server" AppendDataBoundItems="true">
    <asp:ListItem Text="<Select Subject>" Value="0" />
</asp:DropDownList>

You could then bind the DropDownList to a DataSource in the code-behind (just remember to remove:

ddlSubject.Items.Insert(0, new ListItem("<Select Subject>", "0"));

from the code-behind, or you’ll have two “” items.