Should PUT and DELETE be used in forms?

Your question involves two closely related but separate standards, HTTP and HTML. The PUT and DELETE methods are part of HTTP. In HTTP they have obvious use in RESTful interfaces, and other services which build on HTTP such as Webdav.

HTML up to version 4 only defines the use of POST and GET for forms. HTML5 at this time appears as though it may support the further methods. [note, support is not included in the current w3 draft]

Any current browser support (I'm not directly aware of any) will be very limited and only really useful as an experiment at the bleeding edge.

GET, POST, PUT and DELETE (there are others) are a part of the HTTP standard, but you are limited to GET and POST in HTML forms at this time.

As Andrew mentioned, you can use PUT and DELETE in AJAX requests; however, this only works in some browsers (see http://api.jquery.com/jQuery.ajax/).