Cell phone towers use directional antennas. They focus most of their transmitting and receiving energy in the horizontal direction, like this image shows:
Generally speaking, cell phones will usually work at an altitude below 5,000 feet or so. Once you get above that, you get a weaker and weaker connection to the cell towers, drastically reducing your chance of a successful connection. It’s almost impossible to get a decent connection once you get above 10,000 feet. You might get lucky and get a good signal bounce or catch an antenna sidelobe, but the chances of your cell phone connecting at those altitudes is pretty small.
IIRC, all of the 9/11 calls were made at an altitude below 5,000 feet.
In the early days of cell phones, an airborne cell phone used to wreak havoc on cell phone systems. As I understand it, the biggest problem was more that the phones were connecting to multiple systems simultaneously, not that it was connecting to multiple towers or that it was moving fast and switching rapidly between towers. Since cell phone users are a generally obnoxious bunch (it often seems like the best way to guarantee that someone will use a cell phone in a particular area is to hang a sign there saying that cell phone use there is prohibited), the cell phone companies just had to cope with the problems, and they ironed out all of the problems and redesigned the systems so that they could handle an airborne phone without any problems. An airborne cell phone hasn’t been a major worry for cell systems in a very long time.
The FCC doesn’t like airborne cell phones because they tie up resources in multiple towers simultaneously, reducing the overall bandwidth available for other users. The FCC ban on cell phones cites this as a reason, and also cites the FAA’s concern for the potential for interference with aircraft systems. Despite what some folks say, cell phones really can cause interference to aircraft systems, though since modern planes are designed with potential interference from cell phones in mind, the chances if a cell phone causing an actual problem are fairly rare.
Cell phones these days will vary their transmitting power in order to save battery life. If they are talking to a tower some distance away, they will crank up their transmitting power so that the remote tower can hear their signal. If they are talking to a tower that is close and can easily hear them, they’ll drop their transmitting power to save battery life. Some airlines are experimenting with picocells, as was already mentioned, since not only does this allow the airplane to provide service to passengers who want it, but it also drastically reduces interference from cell phones since all of the phones on the plane will reduce their transmitting power.