Killing an enemy Civ entirely only really achieves two things (other than cities).
- It takes them out of the game.
If they were close to some kind of noncombat victory, then they can't win if they are destroyed. If they were really close, they may have been able to scrape in ahead of you with that last city.
It also means you don't have to worry about them building up again and coming after you, or forming an alliance to come after you etc. (of course, see 2 below).
- You gain Warmonger points.
The other thing you "gain" is everyone else hates you.
It looks like you gain additional bonus Warmonger points for wiping out enemy Civs. This would often offset any bonus from 1, because you would face an increasingly hostile world.