My wife and I purchased an older house with the popcorn ceilings, as well. We don't like the looks, and so we decided to deal with it. We took two samples and sent them away for testing. The ceiling has 2% asbestos, which is not much, but enough to require HazMat removal (expensive).
If you just paint the ceiling, you should have no problems. However, if you ever want to put a light fixture in the ceiling, or hang a plant, or do anything like that, you run the risk of stirring up some of the asbestos. Before buying the house, I would ask the current owners if you can take a sample for testing. If it turns out to be asbestos-containing, you should drop your offer price to cover the cost of removal. Our sellers met us half-way on the total removal cost.