Aren't non-polarized plugs a little dangerous? Why still use them?

In the US, there is a "symbol" of a square inside of a square that stands for "Double Insulated". You can find these on mains powered devices that have a chassis that is mechanically designed to keep power from reaching any conductors on the outer housing (The part the user touches). Cell phone adapters are not polarized because the connector that you attach to the phone is isolated by a transformer. This keeps the mains voltage away from the user. Also besides safety, when using a bridge rectifier to convert the AC to DC, the bridge doesn't care which side of it gets the "hot" line and which gets the "neutral" line.