Some people don't like to bombard, but the more I use it and the higher levels I play, the more I say "bomb the hell out of the city and THEN Take it."
Here's my tactical analysis of why to bombard a city before taking it.
1) Cultural improvements in a city are not kept when you take it over. They are wiped out. The AI rarely builds mass transit systems or factories so usually in a big city you end up with a barracks, bank and market place (and harbor if its costal). You'll never lose a hospital or aquaduct, probably because it would cause too many design problems for the programers to handle large cities without them
So basically you lose 3/4 decent improvements. The earlier the age, the less likely you are to see those improvements anyway, so that leaves less. By the time you are in the modern age, there is an excellent chance that you've maximized your production and minimized corruption so you can probably rebuild anyway, or corruption is so rampant that far away that having a bank is not going to help much. So overall, and late in the game an airport would be better than a harbor unless you really need to be able to heal sea units, and you rarely see an airport in an AI city.
So what are you left with? You lose a barracks and a marketplace. They can be rebuild in 3-6 turns depending on how bad you want to rush them when you remake them. (barracks-library/temple-airport-marketplace in whatever order you want to rush depending on need). Also note that a market place is not a strategic necessity either.
2) A 25 person city is hard to take. 100% defensive bonus plus once you take it the city will riot tremendously. A rioting/resisting city will culture flip pretty easily, especially deep in enemy territory. However, culture flips are easier to prevent it you bomb the heck out of the population. You get the population down, and then stick a few units in it and advance with the rest of your stack.
In the early ages, you want the population because they can be made to produce things for you. By the time you get late in the game your production in those cities will probably be nonexistant due to corruption so the number of people don't matter. The best production I got out of a city with a WLTK day was 7 shields after rushing all improvements in a very afar away city, though oddly enough it dropped to 5 a few turns later even when the WLTK day was still going.
3) So if you aren't going to get much out of a city, why take it? Three reasons.
a) location
b) location
c) location
If you are fighting a late age war, the only reason to take a city is strategic location. You can't always just raze a city and drop a settler their either late in the game because the enemy's culture is too wide and will simply overlap over the previous city you just razed. Using cities to springboard from is the fastest way to wipe out your enemy. And I do mean wipe out. By the time you get tanks and artillery and infantry, it is my opinion that the way to win a war most effectively is with total war. Wipe out the population, destroy their culture, their improvements, keep only the resources you need to continue your war, which are the location of the city and the roads and railroads you need to keep moving. All else gives you nothing and carries too great a risk to maintain.
Hell war is pretty pointless after a while too. Why take cities when you can't keep them low in corruption? You get war declared? Drop a few nukes, bomb the units and cities on the border, take a few, then give them back the city like giving back a hankerchief after you've sneezed into it as a "gesture of good will."
