Meguillat Esther is, famously, the one Tanakh text in which the name of G-d is never mentioned. Suppose you had a worn-out printed copy. Could you dispose of it as you would any old book, given the fact that it does not include Shemot? Or would it, as a holy text and/or an object used for a mitzvah (talmud Torah) require genizah?
Rabbinical Assembly (Conservative) says yes.
Rabbi Joe Blair (Reform or Reconstructionist?) says maybe.
Din Online (Orthodox) says certainly.
Rashbatz (Shu"t Tashbetz 1:2, quoted by various later authorities) says it would require genizah miderabanan.
(All of these sources seem to be dealing with even a non-scroll version of Megillat Esther. Mishnah Berurah 154:22 says that a scroll version of any book of Tanach requires "strict genizah" (see here))