Having a phone on, or let's say, an iPod, won't disturb at all the electronic systems on board of the airplane. Maybe if you're flying a small airplane you'll have a phone doing weird stuff to your headset as someone said below (my personal experience is that it only happens when the phone starts transmitting with more power after you lose cell coverage). Or perhaps if it's a very old plane. But not a really big deal.
But when accidents do happen, you'd better be ready, and one of the reasons the FAA hasn't removed this rule yet, is that it forces most users to actually mind about what's happening (during t/o and landing) instead of being looking at their phones or listening to music. In case of an accident, or if an evacuation takes place, everything would happen in under two minutes and it is usually a good thing to have people see by themselves what's happening and ready to listen for instructions (and not disorientated).
Of course your plane won't crash if you're playing Angry Birds during landing. It's just not a good idea to do it.