It seems much has changed with Bombers in Civ4. Can you only destroy tile improvements, not roads? How does one cut off resources then?

IS the capital still necessary for trade, so that pillaging the tiles around it screws up their trade network?

Is there an efficient way to pillage, outside of sending ground troops?

No one makes it to the modern era? Any input would be grand!

You can always just blow up the mine/plantation/well/fort on top of the resource. If there's a road leading to it, but no improvement to harvest it, then the resource is still denied.

Really?? so the improvement is what harvests the resource, not a road, a la Civ3? interesting...

Roads are still necessary, but they're not sufficient. You have to have both an improvement and a road from that improvement to a city--preferably a city within two spaces. That city then needs to be connected--usually by another road--to another city. All such-connected cities benefit from the resource, even if they aren't connected to the captial.

In the last game I played before going back to SMAC, I carved Caesar Augustus in half. The southern part of his empire had Elephants, the northern part had Horses. So one side was only capable of building Elephant Cavalry, while the other was only capable of building Horse Archers.

Yes, it's usually better to bomb the resource improvement tile itself, if you can. Generally speaking these take longer to rebuild than a road; also, the AI tends to build a lot of redundant interconnecting roads, making it hard to cut off a route. And resources adjacent to rivers (with the improvement & within cultural borders of course) will automatically be transported to any city along that river, as well as any coastal cities on the same coast that the river empties to.