With a lot of disasters, cell phone systems get over loaded because so many people start trying to use them at the same time. You also need the surface infrastructure to support their use.
So -- no space rocks, no EMP / nuke, no tidal wave, no earthquake...
The best and easiest would be things that kill a lot of people without knocking down a lot of the buildings. Zombies are a good one. Really, any kind of massive illness will do. Illness is really good because it keeps a few people alive to keep the infrastructure up. You still need power to the towers, which means you still need power plants.