Ciao e grazie di avermi risposto ora ti posto la classe
puoi spiegarti meglio dove sbaglio grazie


codice:
public class Frame extends JFrame {
 static ResultSet rs2;
  int righe=0;
  int c=0;
    Object[][] value=new Object[righe][2];
    String[] columnNames={"nome","cognome"};

  public Frame() {
    
    
    
    
    getContentPane().add(jScrollPane1, java.awt.BorderLayout.CENTER);
      jScrollPane1.getViewport().add(jTable1);
      setDefaultCloseOperation(EXIT_ON_CLOSE);
      setTitle("Rirsultati Tabella");
      pack();
      setVisible(true);
      connetti();
      ritorna();
  }

  public static void main(String[] args) {
    Frame frame = new Frame();
  }

  JScrollPane jScrollPane1 = new JScrollPane();
  JTable jTable1 = new JTable(value,columnNames);

   public void connetti(){
     Connection connection = null;
     String codice="";
     int id=0;
     int i=0;
       try {
        String databaseURI = "jdbc:mysql://localhost:3306/archivio";
        String userName = "root";
        String password = "";
        Driver driver = new org.gjt.mm.mysql.Driver();
        DriverManager.registerDriver(driver);
        connection = DriverManager.getConnection(databaseURI, userName,
                                                 password);
        if (!connection.isClosed())
          System.out.println("Connesso!");
        } catch(Exception  e) {
        System.err.println("Exception: " + e.getMessage());
        }
        try {
          Statement st = connection.createStatement();
          String query = "SELECT * FROM tabella";
          ResultSet rs = st.executeQuery(query);
          while(rs.next()){
                   value[i][0]=rs.getString("nome");
                   value[i][1]=rs.getString("cognome");
                   i++;
                 }
      
                          

        }catch(SQLException je){}  

   }


   public void ritorna(){
    Connection connection = null;
           try {
               Statement st = connection.createStatement();
               String query = "SELECT * FROM tabella";
               ResultSet rs = st.executeQuery(query);
   
               rs2=st.executeQuery("SELECT COUNT (*) as c FROM tabella");
               rs2.next();
               righe=rs2.getInt("c");
   
   
             }catch(SQLException ve){}
   
   
   }

}