Despite being traditionally taught as a fully invasive holy war, it seems like there would be a great deal of exchange between participants on both sides. What were areas where the 'invaders' showed appreciation for concepts, tools, or practices of the populations already living there? This could include Islam, but also Judaism and any other alternative thought models in operation at the time.
The era of the first, successful (from the Latin POV) crusades--11th/12th centuries--brought everyday western Christians, not just a bare handful of traders, into sustained contact with Islamic civilization on three frontiers of conquest: the Near East, Iberia, and Sicily.
The most famous zone of exchange, or at least Latin absorption of Arabic knowledge, is intellectual. Muslim scholars in the schools and courts of Christian Iberia and Sicily supplied and studied Arabic translations of ancient Greek texts as well as original Muslim scholarship. This has been pretty well covered on /r/AskHistorians and elsewhere, so I'll concentrate on some other topics.
Sicily under the Normans frequently looked to the Islamic world, above all Fatamid Egypt, for insight on governing a multireligious territory--and to build a PR campaign for itself! In many ways, the early Norman rulers modeled their treatment of their Muslim population on the Islamic dhimmi system of dealing with Jews and Christians, setting up a parallel tax system, for example. To adorn their churches and monuments, they actually imported artists and artisans directly from (especially) Constantinople and still-Umayyad Cordoba (Iberia). The Norman administration recruited scribes and scholars--including quite a few eunuchs, /u/caffarelli--from Cairo. Indeed, the first generation of Latin lords of Sicily governed in Arabic.
Later on, they issued charters in Latin, but used Arabic as a prestige language in sections. The charters reflected contemporary Fatamid practice in several ways, including the use of extremely hyperbolic titles to augment the rulers' prestige, standard formulae of piety translated almost directly from Arabic to Latin, and impersonal and indirect references to various people involved. Roger II conducted public appearances dressed in Egyptian-style robes. Muslim chronicler Ibn Jubayer compared William II's court to that of any good Muslim ruler! Overall, the Normans really sought to portray themselves publicly a la the Fatamids in Egypt, whom they viewed as the most "together" and prestigious government.
My very favorite example of cultural exchange, though, does come from the Near East. For a long time, the traditional line in scholarship was that the Christian conquering/ruling class didn't really interact with the Muslim population. As so often happens, paying attention to women and dicussions of women in the sources has helped overturn this. Turns out, chroniclers from the crusader states in modern-day Syria rant and rave about Christian women in particular starting to dress like Muslims. How will Christian men ever tell them apart when it comes time to get married?
For their part, the Muslims were more concerned about men's beards.
As well as ideas and practices, some products were introduced into Europe as a result of the Crusades. Sugar (which had originated in India), rice, paper (which was invented in China), were all discovered in the Middle East by European crusaders, and introduced into Europe.