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.
As of September 2022, latest HTML specs and drafts still don't have support for methods other than GET and POST by default. If you don't use a method middleware, you are stuck with these two options. (method attribute can also have 'dialog' as a value, but it is irrelevant since it is not directly related to HTTP methods.)