Would like to have the ability to save different versions of a form, something like a button "Save As".

Unrelated, is there a way to do some kind of "save as" so I can make
different versions of a form?
Thanks!

No, there is no a way to save different versions of your form, at least using a button "Save As", you can clone your forms and have different versions, make changes on each one and you will find them in "My Forms" section, this guide will help you to cloned an existing form from your account: http://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account.

However, I will escalate this as a feature request so our developers will take it into account and depending on the amount of users requesting the same then it may be developed, if it is, we will let you know via this thread.

 

Besides to what Keving has indicated, you can also use the Revision History, in case you would like the form to turn back to a previous version,

https://www.jotform.com/help/294-How-to-View-Form-Revision-History