My advice is to end as soon after the climax as possible. Once they've done whatever the campaign goal was, they have the whole emotional payoff of basically WINNING. Narrate the rewards, do the crowning ceremony, show how what they did matter, and then cut it off. There is nothing more disappointing than having stopped the end of the universe as we know it, becoming a baron of the thanelands and receiving that staff of the archmagi you were lusting for, and then having to go off and kill more random crap, because apparently saving the world wasn't enough.
Later, in another campaign, they can hear about the legends of their PCs, but once they've gotten the massive reward they were going for, they have little more to fight for. Plus, your whole campaign has been working towards the climax, in a multi-year build up, any threats after that are going to be disappointing by comparison.
So, yeah, give them the rewards you know they want, the flashy recognition, the titles and the loot, and the end it. Narrate a small epilogue, showing how what they did changed/preserved the world and the segue into the next campaign.