Yes, but most of the time, they usually submit themselves to become a vassal of another civ right before you can finish them off. Then by the time you realize it, the strongest civ declares war on you on the very next turn
Amen to that.
You have to check constantly to see if they will capitulate. Every turn. Twice.
I check once during the turn and once again right before I end it.
The worst thing in the world is when I'm warring someone and making headway, then they capitulate to the lead civ and I'm suddenly at war with both of them.
Stupid, now I'm losing ground where I was gaining moments ago.
Personally, though I think the situation sucks, I think it's a nice touch to the game that makes you a little more discretionary with your wars and diplomacy, so I leave vassals enabled.
Sometimes you can get an enemy to capitulate without doing that much damage to them at all.
Once, while playing as Ghandi on Prince, I was in the point and power lead. I declared war on Brennus and his little vassal Fredrick (whom I had crushed but failed to get his capitulation, ironically). Brennus was in the third spot.
I set my cavalry on auto-pillage (explore) and let them go to work since I had more than plenty of them to spare for a while. About five turns later more than half of his empire was completely devoid of improvements, but I had not taken any cities or destroyed more than five or six units, and he offered to capitulate, with 1000+ gold and a map.
I was bigger than he was anyway, so I wasn't worried about him growing out of my protection, so the vassalage was pretty much permanent and he himself was nearly at full strength!
It was awesome. From that point on I would declare on everyone and watch Brennus take them out for me. I would move my cavalry in behind his forces to take cities (and make sure he didn't "grow free").
Vassal states have their uses, so long as you allow them to have a little breathing room.