loadFiles("Documents/2013",
        function(files) {
           var zip = new JSZip();
           zipFiles(zip,files,0,function(content){
               console.log('Done.');
               saveAs(content, "archive.zip");
           });
        },
        function(sender,args){
            console.log(args.get_message());
        }
    );

function zipFiles(zip,files,index,complete){
    index = index || 0;
    var curFile = files.get_item(index);
    JSZipUtils.getBinaryContent(curFile.get_serverRelativeUrl(), function (err, data) {
       if(err) {
           throw err; // or handle the error
       }
       zip.file(curFile.get_name(), data, {binary:true});
       index++;
       if(index < files.get_count()) {
         zipFiles(zip,files,index,complete);
       }
       else {
         zip.generateAsync({type:"blob"})
         .then(function(content) {
              complete(content);
         });
       }
    });
}


function loadFiles(folderUrl,success,error){
   var ctx = SP.ClientContext.get_current();
   var web = ctx.get_web();
   var folder = web.getFolderByServerRelativeUrl(folderUrl);
   var files = folder.get_files();
   ctx.load(files);
   ctx.executeQueryAsync(
        function() {
           success(files);
        },
        error);
}