From 1095 until well into the 15th Century the popes regularly proclaimed a series of Crusades --"Holy Wars"-- against various enemies of the Church. The victims of such were initially non-Christians, that is Moslems and pagans, but later Crusades were preached against Christian heretics, and even against quite orthodox folks who happened to have political disputes with the current pope. Cynics have observed that Crusades were the papacy's way of keeping the knights and nobles distracted, les tthey decide to help themselves to the ever-growing wealth and property of the Church. More charitable types have observed that the Crusades exported the most rambuntious nobles and other folks from Europe, leaving the stay-behinds a much more peaceful environment, and don't discount the religious dimension, in a era of extraordinary faith..
At first the object of the Crusades was to recover the Holy Places in what are now Israel and Jordan from the Moslems, who had seized them by force of arms in the 7th Century. The Arabs had been rather tolerant of Christian visitors to the Holy Places, but when the Holy Land fell into Saracen (i.e., Turkish) hands the new overlords had begun to make difficulties. As a result, it did not take much encouragement to send Christian armies off to the Holy Land, in search of salvation, loot, and new lands to rule.
After a false start (the "Beggars' Crusade"), the First Crusade (1095-1099) managed to capture Jerusalem and much else beside, setting up a series of Crusader states to protect their gains. These managed pretty well until 1144, when the counterattacking Moslems took a couple of important Christian strongholds, leading to the Second Crusade (1147-1149), which was a total flop. The Moslem counteroffensive continued, and in 1187 the great Saladin Ayubi recovered Jerusalem for the Sons of the Prophet, sparking the Third Crusade (1189-1192), the most famous --and most effective-- leader of which was England's Richard the Lionhearted. Richard didn't actually recover Jerusalem, but he got on so well with Saladin that the latter agreed to permit unmolested Christian visits to the Holy Places. Unfortunately, Saladin died the following year, and his successors soon began creating problems again. The Fourth Crusade (1202-1204) followed, a most disgraceful affair which ended with the Crusaders capturing and sacking Christian cities, including Constantniople itself, where they set up their own rump version of the Byzantine Empire, which hung on for about 50 years. Things went downhill from there.
Children's Crusade (1212): a spontaneous mass movement of children who thought they could take the Holy Places back with God's help, and mostly ended up as slaves all over the Moslem world.
Fifth Crusade (1217-1221): landed in Egypt (which controlled the Holy Land) and accomplished nothing.
Sixth Crusade (1228-1229): led by the Holy Roman Emperor Frederick II von Hohenstaufen, against the Pope's wishes (Frederick and the pope didn't get along). This was actually a peaceful visit, which led to an agreement permitting Christians free access to the Holy Places.
Seventh Crusade (1248-1254): resulted when the Egyptians Mamelukes routed a local Christian army in 1244. led by Louis IX of France ("Saint Louis"), this also attacked Egypt, but failed amid great suffering.
Eighth Crusade (1270): Louis' second attempt to invade Muslim Africa, which ended in failure when he died.
Ninth Crusade (1271-1272): never actually reached the Holy Land, despite being led by Prince Edward of England (later Edward I).
Acre (modern Akko, in Israel), the last Christian stronghold in the Holy Land fell in 1291. Although several popes preached renewed cursades to liberate the Holy Land, they were mostly unsuccessful. The last expedition generally regarded as a crusade occurred in 1399, when a Christian army marched into the Balkans. After some successes, they were totally routed at Nikopolis, northwest of Constantinople.
The favorite objectives of Crusades were:
Jerusalem. The supreme Holy Place for all Christians.
Egypt, to help liberate Jerusalem, which during this period was under Egyptian political control. In additino, Egypt was a very wealthy place, and provided a good base from which to advance on Jerusalem.
Constantinople, to help fight the Turks, and then go on to bigger things (Jerusalem).
Tunis, to supress Islamic piracy
Spain, a perennial favorite, helping to beat back the infidel, a process that had been going on since the early 8th century, though quiet in this period: Granada is still Muslim.
Crusades were also preached against the remaining pagan tribes in Europe, the Wends, Prussians, and Lithuanians. These began early in the 13th century when the pope authorized the Teutonic Order to "convert" the heathen Slav and Balt tribes to the east. This was an ongoing crusade, with operations nearly every year. The crusaders often did little more than raid into Slav and Balt populated areas, gaining loot and combat experience in the process. Some of the tribes under this attack disappeared (like the original Prussians, a Slavic tribe.) Others converted to Christianity and survived (the Wends are a pocket of Slavs that exist to this day near Berlin.) The Teutonic knights were eager to have knights from other parts of Europe come up and help out. European warriors were equally willing to go crusading against the Slavs and this became something of a rite of passage for many German, English and French knights. It was "great sport" as the Slavs and Balts were not nearly as well organized as the Turks or Arabs. In the 15th century the Slavs and Balts did get organized and dealt the Teutonic order several smashing defeats. The Germans still made attempts to "Drang nach Osten" (move to the east), an attitude that did not come to a halt until Russian troops occupied Berlin in 1945 (and didn't leave until 1994). Many Slavs and Balts are still not sure what what Herman von Salza and his Teutonic knights began in 1226 is truly over. After all, the "crusade" went on for over 700 years.
The most curious crusades were those preached against several enemies of the papacy, most notably against Frederick II von Hohenstaufen . In the 14th century, the French popes in Avignon raised several crusading armies to campaign in Italy against those who supported German, rather than papal, rule. Through this period, the French popes had taken refuge in Avignon, the political situation in the Italian Papal States being too hostile to allow the popes and their servants to live in Rome.
And then there was the Albigensian Crusade.