This would be invaluable with a few additions:

1) Checkboxes (not just radio)
2) email alerts when completed to Form owner(s)
3) Ability to attach files (20-50mb)
4) Ability to turn completed forms into tasks or "to do lists"
5) "if this... then" when creating the questions would be great. So some questions might "unlock" other questions.(slightly different than branching).
6) ability to link dates to a shared calendar (making due dates and reminders possible

It would be helpful to be able to add a GET value to the share link to provide default answers to questions. E.g., ?q1=default&q2=default2

Allow the user to create or auto generate a shortened URL link to send or post.

Include the survey/form within the body of an email message in addition to the link to the survey. Response rates are higher when participants can respond from within the body of an email message.

The ease of use Forms provide would make building request apps, approval apps, and calendar apps much easier.

This feature would allow teachers to share questions with other teachers and to create question banks

I want to transfer ownership of my form to a specific person.

Share the form with specific people.

Especially in corporate setting there is usually a need to send the survey/quiz to specific people instead of everyone in organization. There should be a way to do that.

I've designed a form under "My Forms" to make tests, now I need the final version shared with my company and it would be good to copy same form to "Group Forms" or transfer ownership to group.

We would get much more mileage out of the forms feature if we could pass default values in the form URL that are set when the form opens.

For example we are asking some 100 users to fill out the same form, but some values we want to preset for some groups of users.

Embed a form in outlook so the recipient can automatically answer the form in the email without opening or clicking a link to the form

We are using the form as a guest survey that requires a name and contact information be provided. We offer a prize incentive for anyone completing the survey and need a way to contact the winners.

People are confused by the form having a subheading that says "Your response is anonymous" but the first question requires them to identify themselves.
It would be great to be able to turn that marking off or on depending on the intended use of the form.

I'd like to limit access to the form to specific invitees.

Please provide administrative access across all created forms (for Global Administrators or Forms Administrators) so that the Forms service can be better administered across the enterprise.

Real time data transferring to PowerBI and/or Data Parsing from within Forms.

It would be great if we can give forms prefilled to the user, in order to double check the information needed.

For example, if a I want to share a form to all my friends to ask his birthday date, I want to send the information that I already have (if I have) prefilled in the form.

I suggest Microsoft Forms team to include a "close" button, to end the survey.

You can print to PDF in FORMS but it must be done manually and individually. Google forms sends the PDF form response which can then be saved, which is significantly more efficient than FORMS.