simpleEllasticTextarea.js

function setTextareaHeight(textarea, incCoeff) {
    $textarea = $(textarea);
    var lh = parseInt($textarea.css('line-height'), 10);
    var sh = $textarea[0].scrollHeight;
    var newHeight = sh + lh * incCoeff;
    $textarea.height(lh);
    if ($textarea.height() < newHeight) {
        $textarea.height(newHeight);
    }
}

$('.textarea').keydown(function(ev) {
    if (ev.keyCode === 13) {
        setTextareaHeight(this, 1);
    } else if (ev.keyCode === 8) {
        setTextareaHeight(this, -1);
    }
});