Consider This - Slaying the Big Bad.

An epic adventure or campaign often culminates in a massive battle between the heroes and the main villain of the story. Fun and satisfying. Straightforward and expected.

What happens when someone kills a demigod, demon prince, or arch-devil? Permanently.

Well, some points to consider might be along the lines of:

• Power vacuum needing to be filled. Possibly by a powerful lieutenant or rival.
• An imbalance in the cosmic order. Perhaps this entity truly embodied one or more traits that are now no longer represented in the universe. You've destroyed the Demon Prince of Evil Sawhorses and now evil sawhorses are disappearing from Creation itself. Is this a good thing? Or, even worse, you killed the Demigod of Low Interest Rates.
• From bad to worse. Bet you didn't know that arch-devil you took out was the guardian of the Gate of Inescapable Horror - keeper of the lock that kept a nameless world-devouring monster from entering our dimension. Now that the guardian of the Gate is gone... 
  

Honestly, there are lots of possibilities. But, there have been moments in my own campaign where I wanted more immediate, or intimate, results.

You dealt the final blow to the demigodlike villain of the campaign! What are you gonna do next?! Wait - let's not get ahead of ourselves. Are we treating the Dark Lord of Glitter and Fingernail Clippings as just another fallen foe? Sure - we could do that. But, that's not really my style.

Let's address that particular phrase: "...dealt the final blow..." The DM is free to spread the love around, but the character that laid the villain low should receive the best/worst of what is to come. Where does all the power held by the demigod/demonlord/hellduke go? For my money, most of it will go back to the source - or go nowhere at all. Depends on the circumstances and direction of the campaign. But, some of it will go to the slayer - who will probably never be the same again.

• What was the slain foe known for? Being a powerful warrior? A crafty tactician? A domineering presence? Increase one or more ability scores of the villain's slayer accordingly. To the PC that dealt Asmodeus the killing blow, raise that guy's Charisma - at the very least.
• While you're at it - add some HD to the character. Give them a permanent HP boost.
• It won't all be good. Make the PC toss a saving throw die. Failure indicates an alignment shift toward that of the slain villain's. Eventually, the hero's physical appearance could start to change as well.
• Transfer one or more powers from the villain to the PC. Not necessarily under the character's full control, but definitely something distinctive and disturbing.
• With all this power, it is definitely reasonable to increase the PC's lifespan.
• Give the PC dreams or flashes of "divine inspiration." Harbingers of changes to come. Glimpses of the true workings of reality. Premonitions of danger from divine rivals.
• Did the slain entity have followers or worshipers? Will any of that devotion transfer to the slayer of their deity? Or, will they seek to punish the PC that took away the object of their devotion?

If the campaign is to continue beyond the death of the big bad, it might be fun to have the hero of the hour be the catalyst through which evil continues. The PC might be able to harness the power for good. The PC might fall to a rival. The PC may succumb to evil. The PC could somehow destroy the dark energies within - thus eliminating the threat for all time. In any case, the player gets a truly epic struggle to play. It also gives all the players something to think about as they strive to be the hero that puts down the next great evil.

Consequences. Do we play them?