I think this example [1,2]:

(define-syntax my-or
  (syntax-rules ()
    ((my-or)
     #t)
    ((my-or exp)
     exp)
    ((my-or exp rest ...)
     (let ((t exp))
       (if exp
           exp
           (my-or rest ...))))))

should look like this:

(define-syntax my-or
  (syntax-rules ()
    ((my-or)
     #t)
    ((my-or exp)
     exp)
    ((my-or exp rest ...)
     (let ((t exp))
       (if t                    ; <-
           t
           (my-or rest ...))))))

Otherwise, what's the rationale behind 'let'?

AFAICT, it's described here [3], but Guile is not affected, right?  So
the following works as well:

(define-syntax my-or
  (syntax-rules ()
    ((my-or)
     #t)
    ((my-or exp)
     exp)
    ((my-or exp rest ...)
     (if exp
         exp
         (my-or rest ...)))))

Note that 'my-or' is used in several places (e.g., [4]) and it's
necessary to change them all.  Also, there are other macros that use
'let' (e.g., 'cond1').

[1] https://gnu.org/software/guile/manual/guile.html#Defining-Macros
[2] https://gnu.org/software/guile/manual/guile.html#Hygiene
[3] http://stackoverflow.com/a/3215238
[4] https://gnu.org/software/guile/manual/guile.html#Syntax-Case