Is it possible to create a form that allows for a user to enter multiple records?

Example: a form that mimics a spreadsheet table - and each row of that table is a separate record.

You can check our Spreadsheet widget. 

You can also check Matrix field and Configurable list widget (which will allow your users to dynamically add new fields).

How to Set Up the Configurable List Widget

Before you start creating your form I would suggest you to sign up for a free account.

Please use the next link to sign up:

https://www.jotform.com/signup 

This guide can also help you to create your form:

https://www.jotform.com/help/2-How-to-create-your-first-web-form 

https://www.jotform.com/help/ 

Hope this will help. Let us know if you need further assistance.