우표를 붙이다 is correct. A transitive verb requires an object. An intransitive verb does not require an object. 붙이다 is a causative verb of 붙다 All causative verbs are transitive. If you are uncertain whether a verb is transitive or intransitive, search it with Daum Dictionary(http://dic.daum.net/index.do?dic=kor). You can see it is intransitive(자동사) or transitive(타동사).

The first one, because "붙이다"is a transitive verb, it needs object markers 을/를. \^o^/