You can absolutely use CodePen to build and play with web forms. Due to the sandboxing we do on the preview iframe, you can't actually POST out directly from a form (a minor bit of security), but you can POST directly back to the Pen itself. Like:
<form action="#" method="post"> <!-- go nuts --> </form>
It used to be that if you submitted a form like that, you'd get a gnarly CodePen error. We've fixed that up so that now you'll get a successful POST response, showing you the values submitted.
Certainly more useful than an error page. Let us know if you have any more ideas for it.