It becomes pretty important when you start having to workout resistor networks. It ome in with equivalent circuits, because remember some inputs and outputs of ICs are not ideal, and have resistance. In some circuits you have to take this into account. For example, if you make a resistor divider out of two 10MΩ resistors, and try to measure the voltage with a multimeter, you'll measure less than half the voltage. Why? Because the meter effectively becomes another resistor in parallel with one of the others. And you can use Kirchoffs laws to work out what the voltage would be in that case.
Also, its incorrect to think that any IC will self limit any current flowing through it. While some might have protected outputs/inputs, its not always the case, and there's always ways which will blow them up. Many ICs have let out their magic smoke. So you do have to be careful. That's where datasheets come in, they tell you the limits.