Which HTTP methods require a body?

EDIT: compiled list:

• an entity-body is only present when a message-body is present (section 7.2)
• the presence of a message-body is signaled by the inclusion of a Content-Length or Transfer-Encoding header (section 4.3)
• a message-body must not be included when the specification of the request method does not allow sending an entity-body (section 4.3)
• an entity-body is explicitly forbidden in TRACE requests only, all other request types are unrestricted (section 9, and 9.8 specifically)

For responses, this has been defined:

• whether a message-body is included depends on both request method and response status (section 4.3)
• a message-body is explicitly forbidden in responses to HEAD requests (section 9, and 9.4 specifically)
• a message-body is explicitly forbidden in 1xx (informational), 204 (no content), and 304 (not modified) responses (section 4.3)
• all other responses include a message-body, though it may be of zero length (section 4.3)

This (RFC 7231) Or This version (From IETF & More In-Depth) is what you want. According to the RFC:

For PUT:

The PUT method requests that the enclosed entity be stored under the
supplied Request-URI. If the Request-URI refers to an already existing
resource, the enclosed entity SHOULD be considered as a modified
version of the one residing on the origin server. If the Request-URI
does not point to an existing resource, and that URI is capable of
being defined as a new resource by the requesting user agent, the
origin server can create the resource with that URI. If a new resource
is created, the origin server MUST inform the user agent via the 201
(Created) response. If an existing resource is modified, either the
200 (OK) or 204 (No Content) response codes SHOULD be sent to indicate
successful completion of the request. If the resource could not be
created or modified with the Request-URI, an appropriate error
response SHOULD be given that reflects the nature of the problem. The
recipient of the entity MUST NOT ignore any Content-* (e.g.
Content-Range) headers that it does not understand or implement and
MUST return a 501 (Not Implemented) response in such cases.

And for DELETE:

The DELETE method requests that the origin server delete the resource
identified by the Request-URI. This method MAY be overridden by human
intervention (or other means) on the origin server. The client cannot
be guaranteed that the operation has been carried out, even if the
status code returned from the origin server indicates that the action
has been completed successfully. However, the server SHOULD NOT
indicate success unless, at the time the response is given, it intends
to delete the resource or move it to an inaccessible location.

A successful response SHOULD be 200 (OK) if the response includes an
entity describing the status, 202 (Accepted) if the action has not yet
been enacted, or 204 (No Content) if the action has been enacted but
the response does not include an entity.

If the request passes through a cache and the Request-URI identifies
one or more currently cached entities, those entries SHOULD be treated
as stale. Responses to this method are not cacheable.