Which pope launched the First Crusade in 1095?

Urban II, at Clermont, and no verbatim record of the speech survives - five accounts exist, all written afterwards by people with agendas, and they disagree about what he actually promised. The response was far larger than anything he appears to have intended.

What he seems to have asked for was armed help for the Byzantine emperor, who had requested mercenaries. What departed was a mass movement including large numbers of peasants who set off ahead of the armies, and the first violence of the Crusade was in the Rhineland, where crusading bands massacred Jewish communities in Mainz, Worms and Cologne - months before anyone reached the Middle East, and against the explicit objections of local bishops.

It also gave Europe an idea it had not previously had: that fighting could be penitential. Killing had always required penance; Urban's offer of remission of sin for those who went inverted that, and the theology of holy war was substantially constructed afterwards to justify what had already been promised. Jerusalem fell in 1099 with a massacre that Crusader chroniclers described with enthusiasm, and the memory of it has not finished being politically useful in either direction.