I will either raze or capture depending on the situation or my mood.
But one additional reason for razing is to raze a city to leave a "hole" on the continent. If there is an unpopulated area of the continent, the AI will start building settlers and start walking them to this hole to found a replacement city. Even the idiot AI that you are currently at war with will switch a few cities to settlers and send them towards you with only the token 1 unit guard. Talk about easy slaves. (Note that enemy workers will make a run for it as you get close to them, but the settlers will just march blindly into the bulk of your forces if it sees a spot that needs colonizing.)
So I collect several slaves from my opponent and his equally stupid allies. As for the civs that I am not at war with, I can box those approaching settlers off with my ever growing supply of slave labor, and save them until a war opens up with that civ.
But one additional reason for razing is to raze a city to leave a "hole" on the continent. If there is an unpopulated area of the continent, the AI will start building settlers and start walking them to this hole to found a replacement city. Even the idiot AI that you are currently at war with will switch a few cities to settlers and send them towards you with only the token 1 unit guard. Talk about easy slaves. (Note that enemy workers will make a run for it as you get close to them, but the settlers will just march blindly into the bulk of your forces if it sees a spot that needs colonizing.)
So I collect several slaves from my opponent and his equally stupid allies. As for the civs that I am not at war with, I can box those approaching settlers off with my ever growing supply of slave labor, and save them until a war opens up with that civ.