Module (or code) to display character count? I would like to add a simple character counter on a form textarea.

Is there a module that does this?

I don't want to limit the number of characters that can be input; I only want to display how many characters have been input in the textarea so far.
The Maxlength module has that functionality baked right in:

Maxlength allows you to set maximum length of any field on any form making use of the form API. This includes fields created using the UI. (Example: any text field on a node)
When the maximum length is enforced for a field, while editing content of that type some Java Script will countdown how many characters are left, also if the Javascript is turned off, it falls back to form API validation.

It works great for textfields and textareas alike. This is (roughly) what a textarea looks like after Maxlength is applied: