$(function() {
  $('.report_add').click(function() {
    this_id= this.attr("id");
    $.ajax({
      type: 'POST',
      data: 'reportid'+this_id+'=&userid=789',
      success: function() { ... },
      error: function(){ ... },
      url: '/url/',
      cache:false
    });
  });
});

this_id= this.attr("id");

data: 'reportid'+this_id+'=&userid=789',

var this_id= this.id;

data: 'reportid='+this_id+'&userid=789',

var this_id= $(this).attr("id"); // add a jQuery wrapper

data: 'reportid='+this_id+'&userid=789',

data: 'reportid'+this_id+'=&userid=789',
//-------------^----------^--------------your '=' sign is at wrong place

data: 'reportid='+this_id+'&userid=789',

data: {reportid : this_id, userid : 789},

$(function() {
   $('.report_add').click(function() {
     var this_id= this.id; // <---------update this
     $.ajax({
        type: 'POST',
        data: {reportid : this_id, userid : 789}, // <---- and this
        success: function() { ... },
        error: function(){ ... },
        url: '/url/',
        cache:false
     });
  });
});

$(function() {
  $('.report_add').click(function() {
    this_id= $(this).attr("id");
    $.ajax({
      type: 'POST',
      data: 'reportid'+this_id+'&userid=789',
      success: function() {
      $(this).text('Remove From Favourite');
      },
      error: function(){ ... },
      url: '/url/',
      cache:false
    });
  });
});