Is there anyway to have users of my form recognized as a returning customer?

I'm using the form as an order form.  Is there anyway to have customers register so their common information doesn't have to be re-entered?

Unfortunately there is no way to save the info in this way, I mean there is not a feature that you can either turn on or off, but I think there is a workaround that may help you.

You may display on the Thank You page a link to your users with the most common info pre-populated, you may also indicate them to save this link in case that they want to submit the form again. 

This way you will have some data they submitted pre-filled when they go back to the form opening the link they previously got in the Thank You page and saved.

Here is a guide that will help you to pre-populate form fields: Prepopulating-Fields-to-Your-JotForm-via-URL-Parameters

Here is also another guide that I think may be helpful: How-to-find-field-IDs-and-names

If you have any question, please let us know.