Do Catholics believe that everyone should convert to Christianity for their own salvation? From my understanding it is the Catholic view that all people should be baptized and converted to the Christian faith for their own salvation.

So, for me it follows logically, that Christians envision a world where Christianity is the only religion and all other religions are eliminated. I'm especially referring to non-abrahamic religions like Buddhism and Hinduism. In other words: Do Christians believe that they have to work for a world where there are no more Buddhist practicioners or followers of Hinduism and Christianity is the only religion?

I'm interested in the Roman Catholic point of view. 

EDIT: My question targets towards the implicit cultural imperialism and the implicit goal of destruction of the religious cultures in Buddhist countries and India by the absolutist doctrine of Christianity as the only "right" religion. From my personal perspective, I cannot imagine that it would be God's or Jesus' will to destruct the incredible rich and deep religious cultures of these non-abrahamic religions.
I see many of the other answers here seem a little out of focus. The OP is asking for some Roman Catholic points of view, and while the history lessons are pretty neat, I would rather provide an answer to the OP.

Do Catholics believe that everyone should convert to Christianity for their own salvation?
Yes. Catholics believe that it is better for people to convert and, therefore, gain access to the sacraments. A Catholic believes that his salvation is assured with the sacraments, without sacraments there is no assurance of salvation. 

From the point brought by Geremia. There is only one sacrament required for salvation: Baptism. Baptism is required as it is the only sacrament that removes Original Sin. Original Sin impedes communion with God, which is salvation. Note that a person without moral agency (a baby or small child) would be under Original Sin, so even that person needs to be baptized to achieve salvation upon death. So yes, Geremia is right when he says that you must be baptized, this is not an error as somebody implied. Geremia seems to ignore that the Church teaches three kinds of baptisms: sacramental, blood and desire. This last kind of baptism allows for salvation for non-Catholics; in this case, the term "implicit baptism of desire" is usually used. According to the Catechism of the Catholic Church:


  CCC 1259 For catechumens who die before their Baptism, their explicit
  desire to receive it, together with repentance for their sins, and
  charity, assures them the salvation that they were not able to receive
  through the sacrament.
  
  CCC 1260 “Since Christ died for all, and since all men are in fact
  called to one and the same destiny, which is divine, we must hold that
  the Holy Spirit offers to all the possibility of being made partakers,
  in a way known to God, of the Paschal mystery.”[...] Every man who is
  ignorant of the Gospel of Christ and of his Church, but seeks the
  truth and does the will of God in accordance with his understanding of
  it, can be saved. It may be supposed that such persons would have
  desired Baptism explicitly if they had known its necessity.


Do Christians believe that they have to work for a world where there are no more Buddhist practitioners or followers of Hinduism and Christianity is the only religion? Yes. A Catholic believes that there is only one true religion; and all other religions, although containing stints of truth, may be used by the devil to damn the souls of men. The Catholic also believes in tolerance, and that means that he will put up with other religions, despite their flaws. Something that I believe is much more important for your point of view, is that Catholics firmly believe in the separation of the Church and the State[1]. So a Catholic would never endorse that a state, say a police force, mitigate any kind of religious activity. It should be noted that some religious activity is dangerous, and may be dangerous for society, intervention, in this case, would be endorsed by a Catholic; not for the sake of religious intolerance (i.e. not for the religious activity itself), but for the protection of the weak and vulnerable.

Regarding your point on the destruction of cultural heritage, it should be noted that Catholicism doesn't replace culture. It entwines and mingles, exalting the best aspects of a people's cultural practices and elevating them to a new meaning. You might want to take as an example the work of Franciscan friars to not only preserve, but also promote the Navajo culture through the production of English-Navajo dictionaries and books.

Regarding that God does not will destruction, well you have the wrong religion. The whole point of Catholicism is the destruction of the old man, that is addicted to the world and it's temptations, and the creation of a new man, whose life is directed towards love, and only love. So yes, destruction of habits, customs, and old religions is part of Catholicism. For the Catholics, these things are at a personal level, not at a national or societal level. It is you, a single person the one that must destroy his old self. 

It would be good to remember when dealing with Catholics that it began with the destruction of a single life, and through that death, we may not die.

[1] I've heard this is a recent development, and it might as well be, the oldest reference that I can remember comes from the conquest of the Americas by the Spanish Empire.