There are a couple of options – and which one you pick will depend on your time, your skills, and who your users are…
You could design your own form in your theme, so it’s totally specific to your theme. This gives you the most control over the form, as well as making certain all your users have access to a form. It is, potentially, the one that will require the most effort and time on your part.
You could not provide a form in your theme, but make your theme compatible with one or more of the popular form plugins out there. (Contact Form 7, Ninja Forms, …) Most of those offer an API and/or templates for themes to override. The downside here is that you require your theme users to download one of the supported form plugins if they need a form on their website.
It also depends what you need the form to do: if you just want to offer a generic form functionality to your users, then both the above options will work. If, however, you want to provide a very specific form (a calculator, for instance) then you will have to design your own in your theme – supporting form plugins is not really going to help you in that case.
I hope this helps!