There's a myth out there that Islam converted people by the sword and that the conversions to Christianity in Europe were done voluntarily and peacefully. This isn't exactly the case. The confusion partly comes from the fact that Arabs who were Muslim politically took over the Middle East and became a Muslim ruling class, although they didn't use their position to "convert by the sword" in the conventional sense. People assume that a military conquest is followed up by a forced conversion, but this wasn't the case. Instead, the citizens who were Christian or Jewish, and the area of conquest being the former Roman Empire this included a substantial number of citizens, were allowed to keep their faith as long as they paid a tax. They were prohibited from holding political office, but that was the only disability. This is specified in Islam itself. Gradually over time the people who were once Christians decided to convert to Islam because being Muslim offered greater prestige in a predominately Muslim society, a sociological pressure not something coerced.
The other component of the confusion comes from the fact that in the spread of Christianity in the West there wasn't a Christian state, with the exception of the Teutonic Knights in the Baltic, that came in and conquered the ethnic groups. Groups adopted Christianity on a people by people basis, but that doesn't mean on an individual basis. Instead what happened was that rulers of the different peoples converted to Christianity because of the benefits of being associated with either the Holy Roman Empire or the Byzantine Empire and then imposed their beliefs on their peoples. Information is scarce on how this came about but it seems to be that they sponsored Christianity while letting pagan beliefs exist side by side in a kind of synthesis, with the people's gradually converting to Christianity. Since there were so many groups there may have been forced conversions of peoples to Christianity, only they aren't recorded as forced conversions because it was the kings themselves that were doing it. In the history books forced conversions are only recorded if it was an outside force doing it, for example Charlemagne with the Saxons or the Teutonic Knights with the Prussians and Baltic tribes, as well as the Reconquista.
If they let people have their own beliefs and gradually assimilate to Christianity this would be similar to the conversion process from Christian to Muslim in Muslim ruled lands. If they forced it, well, these would be forced conversions too even though no outside force imposed them, i.e. they were 'self imposed' from the upper classes down.
The Roman Empire had its own history of conversion by the sword (from Wiki):
"After Rome was declared a Christian Empire by Theodosius in 389, laws were passed against pagan practices over the course of the following years. Those who continued to recognize pagan gods were often imprisoned, tortured, and put to death. Many of the ancient pagan temples were subsequently defiled, sacked, and destroyed, or converted into Christian sites. As such, the Christianization attributed to Constantine eventually became a very violent process under Theodosius."
Below are some quotes from good old Wiki dealing with conversion in different countries in Europe, including in Spain. Notice that France, which was part of the Roman Empire itself, has a different history, because the people conquered by the Franks were already Christian:
Unlike the history of Christianity in the Roman Empire, conversion of the Germanic tribes took place "top to bottom", in the sense that missionaries aimed at converting Germanic nobility first, which would then impose their new faith on the general population. This is connected with the sacral position of the king in Germanic paganism: the king is charged with interacting with the divine on behalf of his people, so that the general population saw nothing wrong with their kings choosing their preferred mode of worship.
The Polish state was born in 966 with the baptism of Mieszko I, duke of the Slavic tribe of Polans and founder of the Piast dynasty. His conversion from paganism to Christianity was Poland's first recorded historical event. By 990, when Mieszko officially submitted to the authority of the Holy See, he had transformed his country into one of the strongest powers in Eastern Europe. Mieszko's son Bolesław the Brave built on his father's achievements, for the first time uniting all the provinces that subsequently came to comprise the traditional territory of Poland. In 1025 he became the first king of Poland.
In 486,Clovis I, leader of the Salian Franks, defeated Syagrius at Soissons and subsequently united most of northern and central Gaul under his rule. Clovis then recorded a succession of victories against other Germanic tribes such as the Alamanni at Tolbiac. In 496, he adopted the Roman Catholic form of Christianity. This gave him greater legitimacy and power over his Christian subjects and granted him clerical support against the Visigoths
In 486,Clovis I, leader of the Salian Franks, defeated Syagrius at Soissons and subsequently united most of northern and central Gaul under his rule. Clovis then recorded a succession of victories against other Germanic tribes such as the Alamanni at Tolbiac. In 496, he adopted the Roman Catholic form of Christianity. This gave him greater legitimacy and power over his Christian subjects and granted him clerical support against the Visigoths.
The first Archbishop of Canterbury, Augustine took office in 597. In 601, he baptised the first Anglo-Saxon king, Ethelbert of Kent. The last pagan Anglo-Saxon king, Penda of Mercia, died in 655. The Anglo-Saxon mission on the continent took off in the 8th century, assisting the Christianisation of practically all of the Frankish Empire by AD 800.
Most Muslims and Jews were forced to either convert to Christianity or leave Spain and Portugal and have their assets seized. Many Muslims and Jews moved to North Africa rather than submit to forced conversion. During the Islamic administration, Christians and Jews were allowed to convert or retain their religions with many reduced rights and a token tax, which if not paid the penalty was death, although during the time of the Almoravids and especially the Almohads they were also treated badly, in contrast to the policies of the earlier Umayyad rulers.
The new Christian hierarchy, on the other hand, demanded heavy taxes and gave them nominal rights, but only in heavily Islamic regions, such as Granada, until their own power was sufficient, and the influence of the Inquisition strong enough, to make further expulsion both possible and economically feasible. In 1496, under Archbishop Hernando de Talavera, even the Muslim population of Granada was forced to accept Christianity. In 1502, the Catholic Kings declared submission to Catholicism officially compulsory in Castilian domains. Emperor Charles V did the same for the Kingdom of Aragon in 1526.
Most Muslims and Jews were forced to either convert to Christianity or leave Spain and Portugal and have their assets seized. Many Muslims and Jews moved to North Africa rather than submit to forced conversion. During the Islamic administration, Christians and Jews were allowed to convert or retain their religions with many reduced rights and a token tax, which if not paid the penalty was death, although during the time of the Almoravids and especially the Almohads they were also treated badly, in contrast to the policies of the earlier Umayyad rulers."
Wahabi Islam, which is what bin Laden and the Taliban adhere to, is unique in actually advocating conversion by the sword. However, they are a distinct minority in Islam and their beliefs should not be conflated with either those of most Muslims today or those of Muslims in most of the history of Islam, since Wahabbi Islam only arose at the end of the 18th century.
There are other controversial features of Islamic history. For instance, the status of Zoroastrianism and Paganism under Muslim states. Islam only protects Christianity and Judaism. Another controversy is the "boy tax" levied under several Muslim dynasties, including the Fatimid and Ottoman, which essentially forced Christian communties to give up a certain number of young boys who were then raised by the state to either be military commanders or to be part of the bureaucracy.
Update: it appears that Muslim rulers did forceably convert pagans. However, although this is significant, it should be remembered that at the time that Islam started most of the territories that would become Muslim had already been forced to become Christian by virtue of being part of the Roman Empire. This includes Syria, Jordan, Palestine, Lebanon, Egypt, Algeria, Tunisia, Libya. The Wiki article on the concept of Dhimmi is very good at chronicling the ins and outs of religious restrictions and incidences of forced conversion under Islam, which is surprising considering the political climate.