Will current pass without any resistance?
A wire is just a very small resistor. The limiting case is a superconductor. So, ask yourself what happens in these circuits:







simulate this circuit &ndash; Schematic created using CircuitLab

You know that the current in a resistor is given by Ohm's law:

$$ I = \frac{E}{R} $$

So as \$R \to 0\$, then \$I \to \infty\$. When \$R=0\$, then you are dividing by zero and the universe explodes. Fortunately, all wires and things we use as voltage sources (batteries, lab power supplies, wall warts...) have some (very small) resistance, so this doesn't happen in practice.

To know what the use of resistance is, consider what would happen if we had none. Voltage is the result of current that wants to flow, but can't. If there were no resistance, then all the current in the universe could flow, and pretty soon, all the electrical energy in the universe would be depleted, leaving you with no voltage anywhere, and no way to do any electrical work.

As long as we are considering what happens as the resistance gets smaller, we might as well consider what happens as it gets bigger:







simulate this circuit

That is, as the resistance gets higher, less current flows. As \$R \to \infty\$, \$I \to 0\$. When \$R = \infty\$, you have an open circuit, and no current flows. This is just the case of a battery sitting on your desk. There's also no work being done in this case, because although the voltage is exerting a force on the charge in the circuit, it can't move it.