Based on http://html5-demos.appspot.com/static/a.download.html: ^(archived)

var fileContent = "My epic novel that I don't want to lose.";
var bb = new Blob([fileContent ], { type: 'text/plain' });
var a = document.createElement('a');
a.download = 'download.txt';
a.href = window.URL.createObjectURL(bb);
a.click();

Modified the original fiddle: http://jsfiddle.net/9av2mfjx/

You can create files in browser using Blob and URL.createObjectURL. All recent browsers support this.

You can not directly save the file you create, since that would cause massive security problems, but you can provide it as a download link for the user. You can suggest a file name via the download attribute of the link, in browsers that support the download attribute. As with any other download, the user downloading the file will have the final say on the file name though.

Copyvar textFile = null,
  makeTextFile = function (text) {
    var data = new Blob([text], {type: 'text/plain'});

    // If we are replacing a previously generated file we need to
    // manually revoke the object URL to avoid memory leaks.
    if (textFile !== null) {
      window.URL.revokeObjectURL(textFile);
    }

    textFile = window.URL.createObjectURL(data);

    // returns a URL you can use as a href
    return textFile;
  };

Here's an example that uses this technique to save arbitrary text from a textarea.

If you want to immediately initiate the download instead of requiring the user to click on a link, you can use mouse events to simulate a mouse click on the link as Lifecube's answer did. I've created an updated example that uses this technique.

Copy  var create = document.getElementById('create'),
    textbox = document.getElementById('textbox');

  create.addEventListener('click', function () {
    var link = document.createElement('a');
    link.setAttribute('download', 'info.txt');
    link.href = makeTextFile(textbox.value);
    document.body.appendChild(link);

    // wait for the link to be added to the document
    window.requestAnimationFrame(function () {
      var event = new MouseEvent('click');
      link.dispatchEvent(event);
      document.body.removeChild(link);
    });

  }, false);

Simple solution for HTML5 ready browsers...

Copyfunction download(filename, text) {
    var pom = document.createElement('a');
    pom.setAttribute('href', 'data:text/plain;charset=utf-8,' + encodeURIComponent(text));
    pom.setAttribute('download', filename);

    if (document.createEvent) {
        var event = document.createEvent('MouseEvents');
        event.initEvent('click', true, true);
        pom.dispatchEvent(event);
    }
    else {
        pom.click();
    }
}

Usage

Copydownload('test.txt', 'Hello world!');

Save to filesystem

Have a look at angular-file-saver

Or use the following code as a reference in saving a BLOB. Where the blob object is generated from a JSON Object. But extration to a TEXT file is also possible.

    // export page definition to json file
    $scope.exportToFile = function(){
        var filename = 'filename'       
        var blob = new Blob([angular.toJson(object, true)], {type: 'text/plain'});
        if (window.navigator && window.navigator.msSaveOrOpenBlob) {
            window.navigator.msSaveOrOpenBlob(blob, filename);
        } else{
            var e = document.createEvent('MouseEvents'),
            a = document.createElement('a');
            a.download = filename;
            a.href = window.URL.createObjectURL(blob);
            a.dataset.downloadurl = ['text/json', a.download, a.href].join(':');
            e.initEvent('click', true, false, window, 0, 0, 0, 0, 0, false, false, false, false, 0, null);
            a.dispatchEvent(e);
            // window.URL.revokeObjectURL(a.href); // clean the url.createObjectURL resource
        }
    }

Using LocalStorage

Saving to localStorage:

window.localStorage.setItem('key', value);

Getting from localStorage

window.localStorage.getItem('key');

Delete key from localStorage

window.localStorage.removeItem('key');

Or using the AngularJS module 'ngStorage'

Browser compatibility

Chrome - 4    
Firefox (Gecko) - 3.5    
Internet Explorer - 8    
Opera - 10.50    
Safari (WebKit) - 4

See live example (credits to @cOlz)

https://codepen.io/gMohrin/pen/YZqgQW

You cannot serialize file API object.

Not that it helps with the specific problem, but ... Although I haven't used this, if you look at the article it seems that there are ways (although not supported yet by most browsers) to store the offline image data to some files so as to restore them afterward when the user is online (and not to use localStorage)

I agree with Nathan Hayfield. The browser will handle the save dialog box for you. Setting the header Content-Disposition will send the response back as an attachment and the browser will handle it from there. eg.

content.Headers.Add("Content-Disposition", "attachment; filename=export.csv");