Arguably some of the later crusades, such as the Albigensian Crusade or the Baltic Crusades could be seen as wars that spread Christianity. I say arguably because wars are complex human efforts and there does not seem to be much consensus on the causes of them, because the causes can often be attributed to many factors. As an example, the Thirty Years' War is seen by some as a religious war between Catholics and Protestants, but most historians would now claim the cause to be politics more than religion, per se.

I think a case could be made for the above examples to be wars that spread Christianity however as one of the results of them was the Christianisation of the respective populations - the heretical Cathars in the first case and pagan Baltic peoples in the latter. But even here there is debate. Historians of the Albigensian Crusade have argued that it could be characterised as a civil war in which the northern French nobility, and especially the King of France, achieved political hegemony over the south.

Another example might demonstrate the issues here well: The First Crusade. In most of twentieth-century historiography, the crusading movement was seen as one of material conquest and gain, but in 1987 Jonathan Riley-Smith shifted the conversation by demonstrating that the majority of participants in the First Crusade were devoutly religious. There is plenty of evidence for this. Numerous participants raised the resources to attend by selling their possessions to monasteries and once the objective of capturing Jerusalem was achieved their returned to their homes. This is coupled with Pope Urban II proclaiming heavenly rewards and presenting the effort as a religious pilgrimage with cries of "God wills it!" from the crowds.

However, Bohemond of Taranto kept hold of Antioch when it fell to the army and carved out a sizeable kingdom in the surrounding area. To complicate matters more, it has been suggested that Pope Urban II's motive was to increase papal power in the wake of the investiture controversy. Going deeper, the First Crusade emerges out of the Byzantine Emperor Alexios I Komnenos sending envoys to the West asking for some Latin mercenaries to help with the reconquest of territory lost to the Seljuk Turks.

The First Crusade, perhaps the archetypal "Holy War" is thus more complicated than being purely a war fought for God and for no-one was the aim to convert the Holy Land back to Christianity.

In fact, the whole area is very complicated. You mention Jihad - an Arabic term meaning "struggle". It has multiple meanings, ranging from the struggle to live an authentically pious life, to the Holy War concept that it is well-known for in the West today. Many historians would challenge the concept of Islam spreading by the sword, and to some extent this is not because it did not spread as a result of the Arab conquests, but that the Arab conquests might not have been primarily wars that aimed to spread the religion. This is all keenly debated but one view is that the Arab conquests were as much about capturing war booty and establishing Islamic political hegemony. The populations of those conquered were not required to convert and at the beginning the Muslim Arabs were garrisoned away from the population centres. Now, this view is not uniform and also has its critics, but it serves to show that war and the spread of religion are comple affairs.

There is a lot more that could be said - concepts about Just War for example, or attitudes towards pacifism, but this summary might help with your initial question as phrased.