It works great and is one of my favorite things to do in the game. Theaters really help a lot to increase culture, and are relatively inexpensive to build. Great artists doing their Great Works in a city can help too. Universities and libraries help too, as I recall. Also shrines.
I've gained a city or two doing this, and it's a pretty cool reward. When the AI plants a city right on my borders, I often crank up the culture by building shrines, theaters, etc. When starting a new city, often the first thing I will do is work on culture to get a few extra unclaimed squares or steal a few from the enemy. Every time you get some from the enemy, he should have a less strong city and culture overall, whereas yours becomes stronger, making the rest of the stealing easier.
I often try to send missionaries through civs with open borders with me, to help turn over cities and prevent tensions. Having a different religion is a huge arguing point for civs, so eliminating that makes civs less likely to bug me and more likely to just suddenly give me their cities.
It can be sudden, too. A city will sometimes keel over even if I haven't been doing anything that seemed cultural to me.
One thing about great artists -- they can be a waste in a city that is just overpowered by stronger neighbors. I have had great artists build their works and gotten the message that my borders have expanded, without them visibily expanding even a single square into enemy territory. All I did was expand the power of the city within my own borders.
