Can I make a textarea grow with text to a max height?

You can use contenteditable and let the user input in a straight div, here’s a demo: http://jsfiddle.net/gD5jy/

HTML

<div contenteditable>
    type here...
</div>

CSS

div[contenteditable]{
    border: 1px solid black;
    max-height: 200px;
    overflow: auto;
}