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."

History would support that position.

In the mid 15th century, Tomás de Torquemada, as head of the Spanish Inquisition, converted tens of thousands of Jews and others to Catholicism. Most of them converted under threat of torture and death. Actual belief or lifestyle didn't matter much; what was important was public confession, acceptance of Christ, and baptism. The sacraments of the Church would then lead these converts to salvation.

With full support of the Church and the Inquisition, Latin America was completely taken over by Spain and Portugal. Almost all the original inhabitants were slaughtered or assimilated, conversion to Catholicism being the justifying force:

Castilian law prohibited foreigners and non-Catholics from settling in the New World. However, not all conquistadors were Castilian. Many foreigners Hispanicised their names and/or converted to Catholicism to serve the Castilian Crown.
…
Catholic religious orders that participated and supported the exploration, evangelizing and pacifying, … . The Franciscans used a method of mass conversion, sometimes baptizing many thousands of Indians in a day. — Wikipedia: Conquistador

In the 19th and 20th Century, residential schools were established, mostly by the Catholic Church, in Canada, USA, Australia, and other recently settled countries. Children were forcibly removed from their parents, forbidden to speak their first language, and deprived of their culture. For most, the experience was a life of torture and abuse. Again, baptism into the Church and removal from heathen influences was the justification:

Many of the government-operated residential schools were run by churches of various denominations, with the majority administered by Roman Catholics. […] The government provided facilities and maintenance, while the churches provided teachers and their own lesson-planning. As a result, the number of schools per denomination was less a reflection of their presence in the general population, but rather their legacy of missionary work. — Wikipedia: Canadian Indian residential school system

A similar position was taken by Mother Teresa in the 20th century. She "converted" countless Hindus to Catholicism by taking sick and destitute children into her clinics and palliative care centers. She sincerely believed that "Suffering is a gift from God.", and used this philosophy on her converts. Many that would have otherwise survived became sick and eventually died under her care. Dirty needles and other medical equipment were continually reused during medical treatment, ensuring the spread of disease, and those that suffered in pain were denied pain relieving drugs. The obvious poverty and inadequate facilities made it easy to solicit millions of dollars in donations, which, rather than being used to improve the quality of care, were used to open more and more centers. At its peak, thousands of nuns worked at over 600 shelters and missions. Saving souls by "converting" Hindus to Catholicism was her overriding goal, a goal obviously shared by the Vatican, which eventually honoured her work with sainthood.

For more details, see my "Lie — Mother Teresa was a wonderful saintly person" and Wikipedia's "Criticism of Mother Teresa".

These examples illustrate that the Catholic church's philosophy includes baptising as many people as possible (even if forcibly) in order to make their souls eligible for salvation by the Church's sacraments.

While from a non-Catholic viewpoint, this philosophy can be seen in a very negative way, from a Catholic position, where it is the Church itself that has the power to save or condemn individuals, this is not at all an unreasonable way of achieving their goal of converting people to Catholicism for the salvation of their souls.

Although some Catholics believe "there is no salvation outside the Catholic Church", there is a newish Catholic teaching that goes like this:

16. Finally, those who have not yet received the Gospel are related in various ways to the people of God.(18*) In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh.(125) On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues.(126) But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Muslims, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things,(127) and as Saviour wills that all men be saved.(128)

Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience. Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life. Lumen gentium P16

So to answer the OP question, there was no doubt violence and forced conversions in the past like with the Crusades, but the Catholic Church now believes God otherwise. This is shown in the bottom block quote from Lumen Gentium P16, starting with "Those [of non-Abrahamic religions] also can ..."

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.