If the circuit contains different wires or different resistors, the line will still be straight but it will be more or less steep, with a bigger resistor having a less steep line and a smaller resistor having a steeper line.
If the circuit contains a filament lamp, which is just a light bulb with a very thin metal filament, the curve gets less steep as the current increases because the wire heats up and its resistance increases.
Diodes are devices that only allow current to flow in one direction, so they only show a current when the potential difference is positive, doing this by having a really high resistance in the reverse direction.