I am interested in what denominations allow or require the belief that hell is the annihilation of a conditionally immortal soul rather than the eternal suffering or eventual redemption of such.
From the wikipedia article on Annihilationism (4th paragraph):
Some Christian denominations which are annihilationist were influenced by the Millerite/Adventist movement of the mid-19th century. These include the Seventh-day Adventists, Bible Students, Christadelphians and the various Advent Christian churches. Additionally, the Church of England's Doctrine Commission reported in 1995 that "[h]ell is not eternal torment", but "non-being". Some Protestant and Anglican writers have also proposed annihilationist doctrines. (emphasis mine)
Later in the article it cites Jehovah's Witnesses (see this question) and the followers of Herbert Armstrong as other examples