Reading Data from SQL DataBase Table to generic collection

You need to instantiate your object inside while loop
Otherwise you will have same data in the collection
So the code should be

protected void Page_Load(object sender, EventArgs e)
{
    List<Student> listid = new List<Student>();
    SqlConnection con = new SqlConnection("........");
    string sql = "select * from StudentInfo";
    con.Open();
    SqlCommand cmd = new SqlCommand(sql, con);
    SqlDataReader dr = cmd.ExecuteReader();
    while (dr.Read())
    {
        Student stud = new Student();
        stud.Studid = Convert.ToInt32(dr["StudId"]);
        stud.StudName = dr["StudName"].ToString();
        stud.StudentDept = dr["StudentDept"].ToString();
        listid.Add(stud);               
    }
    GridView1.DataSource = listid;
    GridView1.DataBind();
}

Also it is not a good practice to use while to data reader or directly open connection
You should use using statement.

using(SqlConnection con = new SqlConnection("connection string"))
{

    con.Open();

    using(SqlCommand cmd = new SqlCommand("SELECT * FROM SomeTable", connection))
    {
        using (SqlDataReader reader = cmd.ExecuteReader())
        {
            if (reader != null)
            {
                while (reader.Read())
                {
                    //do something
                }
            }
        } // reader closed and disposed up here

    } // command disposed here

} //connection closed and disposed here

In the DataReader while loop instantiate a new Student for each row in the database table:

while (dr.Read())
{
 var stud = new Student();
 stud.Studid = Convert.ToInt32(dr["StudId"]);
 stud.StudName = dr["StudName"].ToString();
 stud.StudentDept = dr["StudentDept"].ToString();
 listid.Add(stud);
}