Annihilation of the souls of the damned is something that Jehovah's Witnesses believe in. See the following from the Catholic Encyclopedia:
III. ETERNITY OF HELL.—Many admit the existence of hell, but deny the eternity of its punishment. Conditionalists hold only a hypothetical immortality of the soul, and assert that after undergoing a certain amount of punishment, the souls of the wicked will be annihilated. Among the Gnostics the Valentinians held this doctrine, and later on also Arnobius, the Socinians, many Protestants both in the past and in our own times, especially of late (Edw. White, "Life in Christ", New York, 1877). The Universalists teach that in the end all the damned, at least all human souls, will attain beatitude (apokatastasis ton panton, restitutio omnium, according to Origen). This was a tenet of the Origenists and the Misericordes of whom St. Augustine speaks (De Civ. Dei, XXI, xviii, n. 1, in P.L., XLI, 732). There were individual adherents of this opinion in every century, e.g. Scotus Eriugena; in particular, many rationalistic Protestants of the last centuries defended this belief, e.g. in England, Farrar, "Eternal Hope" (five sermons preached in Westminster Abbey, London and New York, 1878). Among Catholics, Hirscher and Schell have recently expressed the opinion that those who do not die in the state of grace can still be converted after death if they are not too wicked and impenitent.
Holy Writ is quite explicit in teaching the eternity of the pains of hell. The torments of the damned shall last forever and ever (Apoc., xiv, 11; xix, 3; xx, 10). They are everlasting just as are the joys of heaven (Matt., xxv, 46). Of Judas Christ says: "it were better for him, if that man had not been born" (Matt., xxvi, 24). But this would not be true if Judas were ever to be released from hell and admitted to eternal happiness. Again, God says of the damned: "Their worm shall not die, and their fire shall not be quenched" (Is., lxvi, 24; Mark, ix, 43, 45, 47). The fire of hell is repeatedly called eternal and unquenchable. The wrath of God abideth on the damned (John, iii, 36); they are vessels of Divine wrath (Rom., ix, 22); they shall not possess the Kingdom of God (I Cor., vi, 10; Gal. v, 21), etc. The objections adduced from Scripture against this doctrine are so meaningless that they are not worth while discussing in detail. The teaching of the Fathers is not less clear and decisive (cf. Petavius, "De Angelis", III, viii). We merely call to mind the testimony of the martyrs who often declared that they were glad to suffer pain of brief duration in order to escape eternal torments; e.g. "Martyrium Polycarpi", c. ii (cf. Atzberger, "Geschichte", II, 612 sqq.). It is true that Origen fell into error on this point; but precisely for this error he was condemned by the Church (Canones adv. Origenem ex Justiniani libro adv. Origen., can. ix; Hardouin, III, 279 E; Denz., n. 211). In vain attempts were made to undermine the authority of these canons (cf. Diekamp, "Die origenistischen Streitigkeiten", Munster, 1899, 137). Besides, even in Origen we find the orthodox teaching on the eternity of the pains of hell; for in his works the faithful Christian was again and again victorious over the doubting philosopher. Gregory of Nyssa seems to have favored the errors of Origen; many, however, believe that his statements can be shown to be in harmony with Catholic doctrine. But the suspicions that have been cast on some passages of Gregory of Nazianzus and Jerome are decidedly without justification (cf. Pesch, "Theologische Zeitfragen", 2nd series, 190 sqq.). The Church professes her faith in the eternity of the pains of hell in clear terms in the Athanasian Creed (Denz., nn. 40), in authentic doctrinal decisions (Denz., nn. 211, 410, 429, 807, 835, 915), and in count-less passages of her liturgy; she never prays for the damned. Hence, beyond the possibility of doubt, the Church expressly teaches the eternity of the pains of hell as a truth of faith which no one can deny or call in question without manifest heresy.
But what is the attitude of mere reason towards this doctrine? Just as God must appoint some fixed term for the time of trial, after which the just will enter into the secure possession of a happiness that can never again be lost in all eternity, so it is likewise appropriate that after the expiration of that term the wicked will be cut off from all hope of conversion and happiness. For the malice of men cannot compel God to prolong the appointed time of probation and to grant them again and again, without end, the power of deciding their lot for eternity. Any obligation to act in this manner would be unworthy of God, because it would make Him dependent on the caprice of human malice, would rob His threats in great part of their efficacy, and would offer the amplest scope and the strongest incentives to human presumption. God has actually appointed the end of this present life, or the moment of death, as the term of man's probation. For in that moment there takes place in our life an essential and momentous change; from the state of union with the body the soul passes into a life apart. No other sharply defined instant of our life is of like importance. Hence we must conclude that death is the end of our probation; for it is meet that our trial should terminate at a moment of our existence so prominent and significant as to be easily perceived by every man. Accordingly, it is the belief of all people that eternal retribution is dealt out immediately after death. This conviction of mankind is an additional proof of our thesis.—Finally, the preservation of moral and social order would not be sufficiently provided for, if men knew that the time of trial were to be continued after death.