Voltage Required to Ignite 10ohm resistor
DO NOT destructively test resistors or any other devices without the DIRECT SUPERVISION OF AN ADULT QUALIFIED TO INSURE SAFETY

It depends on the wattage rating of the resistor, airflow, atmospheric pressure and composition, what the leads are connected to internally and externally, the temperature coefficient of the resistor, and the degree to which its materials are flame retardant.

DO NOT destructively test resistors or any other devices without the DIRECT SUPERVISION OF AN ADULT QUALIFIED TO INSURE SAFETY

You can find out if you are exceeding the manufacturer's rating by comparing the square of voltage, divided by resistance, to the rated power limit in watts.  For example, 9*9/10 or 8.1 watts is drastically more than the 1/4 watt rating of most small through hole resistors so it's clear that the component is being abused and there is a substantial risk that something bad and potentially dangerous will happen.  (1/2 and 1/8 watt units are also common, though you can get higher rated ones).

DO NOT destructively test resistors or any other devices without the DIRECT SUPERVISION OF AN ADULT QUALIFIED TO INSURE SAFETY

And don't assume the resistor will just burn; it could also explode.  Either one can be hazardous to your health and surrounding property.  Also consider that it could be hot enough ignite other materials or produce nasty gases even if the resistor itself does not burst into flame.  You could also overheat whatever is sourcing power to the resistor.

DO NOT destructively test resistors or any other devices without the DIRECT SUPERVISION OF AN ADULT QUALIFIED TO INSURE SAFETY