Your influence went up for a successful Crusade. Other advantages include:

a) no maintenance cost for anything you got or put into the Crusade till it was over.

b) it could march through territory. If you couldn't reach a province by water or land (b/c you'd have to invade your neighbor first), you could reach it by Crusade.

c) Great crusader units that could only be generated by a crusade and if you let it sit a few turns in a high zeal province, you get lots of free units. Plus if the province is not yours it may suck up the local troops too, including maybe some you could never build.