JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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You can publish you form to you website by getting the code from the embed wizard, I recommend using the iframe method as it will prevent conflicts with similar scripts on your site.
This guide will show you how to achieve this http://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page