Yes, we can definitely embed and HTML code in AEM, So HTML form can also be included in AEM.
As mentioned by Scott, you can certainly create a Form by own or can induce Jquery plugins to do so. But one thing to make sure, to have a service/Servlet to catch the submitted data.
One analogs question's link is :- http://stackoverflow.com/questions/19044506/submit-form-to-servlet-cq5
~kautuk
Kautuk Sahni