8

Scheme, 162 chars
(Line breaks added for clarity—all are optional.)
(let l((s'()))(let((t(read)))(cond((number? t)(l`(,t,@s)))((assq t
`((+,+)(-,-)(*,*)(/,/)))=>(lambda(a)(l`(,((cadr a)(cadr s)(car s))
,@(cddr s)))))(else(car s)))))
Fully-formatted (ungolfed) version:
(let loop ((stack '()))...