If current flows through lowest resistance path, why circuits with grounding still work?
Current flows through ALL paths available.

If the circuit source itself is not connected to ground somehow, you will not be completing a circuit, so no current will flow through you no matter where you touch it.

If the circuit IS attached to ground, then if you touch a live wire some current will go through you. If your resistance to ground is less than the circuits current path to ground at the point you touched it, then more current will pass through YOU than through the circuit. If enough passes though you, you might not be asking any more questions.

So why use grounds at all... You are right, if there were no grounds you would need to touch the circuit in two places to get a shock. However, without a common ground, static could built up and things could be at very different voltages. Moreover, say the switched live in your light switch in your house was shorted to ground, and the neighbors was also, you could actually turn on his light when you turn on yours if things were not grounded back to the transformer. 

Thunder storms could also cause some nasty things to happen without grounds.