<textarea> box to increase height (wrap) when the current text overflows the given width?

Starx

Given that you want to increase text area in its height. It is possible at CSS3 supporting browsers like FF4. You can also control the direction of which it can be resized.

Another of the CSS3 solution can be using contenteditable element, instead of textarea, which will make how you want possible without using any javascript?

I might show you some examples if this is what you want.