A Simple Http Server with Java/Socket?

In addition to the \r\n after every request header line, you have to send an empty line after the header. Example:

out.write("HTTP/1.0 200 OK\r\n");
// Header...
out.write("Last-modified: Fri, 09 Aug 1996 14:21:40 GMT\r\n");
out.write("\r\n"); // The content starts afters this empty line
out.write("<TITLE>Hello!</TITLE>");
// Content...

I corrected your code so that it works (but it is still not perfect, you should handle every request in a seperate thread, e.g. with java.util.concurrent.ThreadPoolExecutor):

public static void main(String[] args) throws Exception {
    // création de la socket
    int port = 1989;
    ServerSocket serverSocket = new ServerSocket(port);
    System.err.println("Serveur lancé sur le port : " + port);

    // repeatedly wait for connections, and process
    while (true) {
        // on reste bloqué sur l'attente d'une demande client
        Socket clientSocket = serverSocket.accept();
        System.err.println("Nouveau client connecté");

        // on ouvre un flux de converation

        BufferedReader in = new BufferedReader(new InputStreamReader(clientSocket.getInputStream()));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(clientSocket.getOutputStream()));

        // chaque fois qu'une donnée est lue sur le réseau on la renvoi sur
        // le flux d'écriture.
        // la donnée lue est donc retournée exactement au même client.
        String s;
        while ((s = in.readLine()) != null) {
            System.out.println(s);
            if (s.isEmpty()) {
                break;
            }
        }

        out.write("HTTP/1.0 200 OK\r\n");
        out.write("Date: Fri, 31 Dec 1999 23:59:59 GMT\r\n");
        out.write("Server: Apache/0.8.4\r\n");
        out.write("Content-Type: text/html\r\n");
        out.write("Content-Length: 59\r\n");
        out.write("Expires: Sat, 01 Jan 2000 00:59:59 GMT\r\n");
        out.write("Last-modified: Fri, 09 Aug 1996 14:21:40 GMT\r\n");
        out.write("\r\n");
        out.write("<TITLE>Exemple</TITLE>");
        out.write("<P>Ceci est une page d'exemple.</P>");

        // on ferme les flux.
        System.err.println("Connexion avec le client terminée");
        out.close();
        in.close();
        clientSocket.close();
    }
}