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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Yes you can create templates by your own and share it to the users, create your form and click "More" -> "Share as Template". Review the following screenshot.
Select Categories for your template, and click "Share Form".
I hope this helps, please let us know if you need further assistance on this, we would be happy to assist you.