I'm not sure if it held for all crusades, but during the 1st Crusade it was very common, and it wasn't exclusive to the Knightly orders which rose up later on. After Urban II called for the retaking of Jerusalem at the Council of Clermont those who pledged to participate wore crosses:
As an outward sign of this pledge they placed the sign of the cross on their clothing--crosses woven of silk and gold or made of the cheapest cloth--worn on the front of their persons when they set out and placed on their backs when they returned home.
From Jill Claster's Sacred Violence
Bohemond of Taranto, one of the leaders in the first crusade, is said to have cut up his finest cloak into crosses to be stitched onto the clothing of his soldiers when he learned of the Crusade, but this might be apocryphal. Whether or not it actually happened, it indicates that Crusaders were expected to wear a cross on their clothing as a symbol of their oath to retake the holy land.
"Whoever, therefore, shall determine upon this holy pilgrimage and shall make his vow to God to that effect and shall offer himself to Him as a, living sacrifice, holy, acceptable unto God, shall wear the sign of the cross of the Lord on his forehead or on his breast. When,' truly',' having fulfilled his vow be wishes to return, let him place the cross on his back between his shoulders. Such, indeed, by the twofold action will fulfill the precept of the Lord, as He commands in the Gospel, "He that taketh not his cross and followeth after me, is not worthy of me." This is the speech of Pope Urban II at Clermont, urging the Frankish nobility to join the First Crusade and "free" the Holy Land. This may explain the first part of your question.
SOURCE: Robert the Monk's account of the speech, written twenty five years after the fact (http://legacy.fordham.edu/halsall/source/urban2a.html)
It’s worth pointing out that medieval people did not use the word “crusade.” A variant form of it in English, “crosiad,” first appears in the late 16th century and “crusade” itself dates only to 1706 according to the OED. In the Middle Ages, to vow to go on crusade—and it was considered a binding, holy vow, like a vow of pilgrimage—someone was “signed with the cross” and became “crucesignatus.” You “took the cross” (crucem accipere, or capere, or recipere, etc.) and then bore it as a visible sign of your vow. Pope Innocent III compared the soft cloth of the crusading cross to the hard wood of the Cross. Some people went a step further. One Englishman had the cross branded on his shoulder as a mark of his vow. One good summary of this: Christopher T. Maier, Crusade Propaganda and Ideology (2004) p. 53.