Here is the small code-snippet which demonstrates how to resize the textarea, so the text could fit its height, without displaying the scrollbars.

var IsIE = document.all?true:false

function textarea_resize(textarea_obj) {
 if (textarea_obj.scrollHeight >= 182) // ~ 12 rows maximum
  textarea_obj.style.overflow = ''
 else {
  if (!IsIE) textarea_obj.style.height = 1
  textarea_obj.style.height = (textarea_obj.scrollHeight + 15) + 'px' // row height ~ 15 pixels
 }
}

Works at least in IE7, FF2/3, Opera 9.