Take a look at the Dev Guide "Creating Status Bar Notifications".

One way to achieve the goal of keeping the icon there only when the application is running is to initialize the notification in onCreate() and call cancel(int) in your onPause() method only ifisFinishing() returns true.

An example:

private static final int NOTIFICATION_EX = 1;
private NotificationManager notificationManager;

@Override
public void onCreate() {
    super.onCreate();

    notificationManager = (NotificationManager) 
        getSystemService(Context.NOTIFICATION_SERVICE);

    int icon = R.drawable.notification_icon;
    CharSequence tickerText = "Hello";
    long when = System.currentTimeMillis();

    Notification notification = new Notification(icon, tickerText, when);

    Context context = getApplicationContext();
    CharSequence contentTitle = "My notification";
    CharSequence contentText = "Hello World!";
    Intent notificationIntent = new Intent(this, MyClass.class);
    PendingIntent contentIntent = PendingIntent.getActivity(this, 
        0, notificationIntent, 0);

    notification.setLatestEventInfo(context, contentTitle, 
        contentText, contentIntent);

    notificationManager.notify(NOTIFICATION_EX, notification);
}

@Override
protected void onPause() {
    super.onPause();
    if (isFinishing()) {
        notificationManager.cancel(NOTIFICATION_EX);
    }
}