All culture producing buildings are destroyed when you capture a city, as well as all military ones (I think, I know Barracks goes, not sure about Stable, Drydock, etc). All other buildings have a percentage chance to be destroyed as well. In fact, thats where the money comes from, its based on what buildings get destroyed.
One cool thing when you play the Inca's, if the Granary makes it, it turns into a culture producing building. Thats nice in those late-game wars, when you want those borders to pop ASAP.
Also note, Wonders, Academies, Scotland Yard, Military Academies, and Shrines always stay, but lose their ability to produce culture, which has been gone over pretty thoroughly in this thread already, heh,