The Eastern Roman (Byzantine) empire was an active participant in the wars of the crusaders. It was the Byzantine emperor Alexios I who arguably provided Pope Urban II with the pretext for calling the first crusade by requesting a mlitary alliance with the Roman Papacy. Byzantine forces aided the crusaders, provided supplies and advisers, and frequently launched their own attacks against Muslim holdings in support of the crusade (and sometimes negotiated with Muslim garrisons to convince them to peacefully surrender to the Byzantines before having to face the often more brutal crusader armies). In the years after the first crusade conquered Jerusalem in 1099, Byzantine royal dynasties frequently intermarried with the crusader nobility of the Kingdom of Jerusalem (and its various counties and principalities). Byzantine involvement in the crusades only came to an end with the fall of the Holy Land to Saladin's armies after the battle of Hattin in 1187.
It is also worth pointing out that a civil war in Constantinople around the year 1200 played a huge role in the fourth crusade. The crusaders were heavily in debt to the Venetians and, to pay for their crusade, sold themselves out as mercenaries to one faction in the Byzantine civil war. As a result, the crusaders sacked Constantinople in 1204, seized huge portions of the empire's lands to rule for themselves, and never actually made it to the Holy Land.