convert json response to javascript array

You can use:

return {events: JSON.parse(msg.d)};

or, for better compatibility:

eval("var result = "+msg.d);
return {events: result};

or jQuery solution

return {events: $.parseJSON(msg.d)};

if msd.d is

 [{"id":1,"title":"Test 1 "},{"id":2,"title":"Test 2"}] 

then you could return it like this:

return {
     events : msg.d
  };

But you would have to do a callback in order to return it. Because ajax is asynchronous. I added the return because that is what you wanted. The alternative would be to make the ajax call synchronous.

I think you just need this:

    success: function (msg) {
        // The event object is what you require
        var eventObj = {events:msg.d};
        document.write(eventObj);
    },

function doXHR( callback ) {
   jQuery.ajax( {
        type: "POST",
        url: "calendar.aspx/get_all_events",
        data: "{}",
        contentType: "application/json; charset=utf-8",
        dataType: "json",
        success: function ( event ) {
            callback && callback( event );
        },
        error: function (XMLHttpRequest, textStatus, errorThrown) {
            alert('Error getting events from database.');
        }
    });
}

doXHR( function( event ) {
    var data = { events: event.d };
    // Do other stuff with data here (processing, displaying, etc.).
    // You can call other functions here and feed them with data.
} );

Note that XHR requests are asynchronous. You cannot simply return XHR request data. You have to put all your further code into callback function so it can process your array when it's available.