Here is a function I just wrote in jQuery to do it - you can port it to Prototype, but they don't support the "liveness" of jQuery so elements added by Ajax requests will not respond.
This version not only expands, but it also contracts when delete or backspace is pressed.
This version relies on jQuery 1.4.2.
Enjoy ;)
Usage:
$("#sometextarea").textareacontrol();
or (any jQuery selector for example)
$("textarea").textareacontrol();
It was tested on Internet Explorer 7/Internet Explorer 8, Firefox 3.5, and Chrome. All works fine.