Motors, HVAC units, welders and a few others are exempted by that via 240.4(G).
Here is a motor example:
2hp 230 volt single phase motor - NEC FLA is 12 amps. Minimum conductor ampacity for general purpose must be 125% of FLA so we need a 15 amp conductor minimum. If we run NM cable we must use 60deg C ampacity values - 14 AWG is acceptable for 15 amps.
Next comes branch circuit short circuit and ground fault protection - this could turn some heads for those not familiar with what is allowed for motor circuits.(see 430.52)
If we have a Standard inverse time circuit breaker we can have up to 250% of motor full load current - which would allow up to a 30 amp breaker on those 14 AWG conductors for this motor circuit.
If we have non time delay fuses we can have up to 300% of motor full load current - which would be 36 amps. We are permitted to go to the next higher standard size in this case which means these 14 AWG conductors can have up to a 40 amp non time delay fuse.
Not all that likely to see a instantaneous trip circuit breaker in a dwelling but if for some reason there would be such a beast installed we can go up to 800% of motor full load current - which is 96 amps. Again we are permitted to go to next standard size so an inverse time breaker on this 14 AWG conductor could be rated up to 100 amps.
Now if the overcurrent devices mentioned above do not allow the motor to start, 430.52 exception 2 does allow for additional increases in the device settings.