How to create a file in memory for user to download, but not through server?

Simple solution for HTML5 ready browsers...

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

  element.style.display = 'none';
  document.body.appendChild(element);

  element.click();

  document.body.removeChild(element);
}

form * {
  display: block;
  margin: 10px;
}

<form onsubmit="download(this['name'].value, this['text'].value)">
  <input type="text" name="name" value="test.txt">
  <textarea name="text"></textarea>
  <input type="submit" value="Download">
</form>

Usage

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

You can use data URIs. Browser support varies; see Wikipedia. Example:

<a href="data:application/octet-stream;charset=utf-16le;base64,//5mAG8AbwAgAGIAYQByAAoA">text file</a>

The octet-stream is to force a download prompt. Otherwise, it will probably open in the browser.

For CSV, you can use:

<a href="data:application/octet-stream,field1%2Cfield2%0Afoo%2Cbar%0Agoo%2Cgai%0A">CSV Octet</a>

Try the jsFiddle demo.

An example for IE 10+, Firefox and Chrome (and without jQuery or any other library):

function save(filename, data) {
    const blob = new Blob([data], {type: 'text/csv'});
    if(window.navigator.msSaveOrOpenBlob) {
        window.navigator.msSaveBlob(blob, filename);
    }
    else{
        const elem = window.document.createElement('a');
        elem.href = window.URL.createObjectURL(blob);
        elem.download = filename;        
        document.body.appendChild(elem);
        elem.click();        
        document.body.removeChild(elem);
    }
}

Note that, depending on your situation, you may also want to call URL.revokeObjectURL after removing elem. According to the docs for URL.createObjectURL:

Each time you call createObjectURL(), a new object URL is created, even if you've already created one for the same object. Each of these must be released by calling URL.revokeObjectURL() when you no longer need them. Browsers will release these automatically when the document is unloaded; however, for optimal performance and memory usage, if there are safe times when you can explicitly unload them, you should do so.