Hello again,
Yes, the inductance has an effect but it does depend on the application as mentioned.
In some apps inductance will hardly have an effect, because the main point is the speed of rotation and the torque. But what we usually like to do is know ALL of the effects and then dismiss any that may not be needed at the time of analysis, not before that.
So what this boils down to is that the there is some inductance, and that inductance may or may not have an effect on the overall system in the given application.
An application that will not feel the significance of the inductance is when the motor is running constantly. The effects of the inductance go away after a short time period, so if it is running constantly the inductance will no longer play a part.
Conversely, connect a large DC motor to a DC power supply with jumper leads and let it run for several seconds, then disconnect the motor and watch the spark fly :-) The spark is due to the inductance mostly.
What this means is that we could make a boost converter out of a motor although it may not be the best :-)
As has been said a PWM application may feel the presence of the inductance much more than a regular constant run motor application, but to take the point home, where we really see a big impact is in a stepper motor application where a good drive circuit takes into account the inductance as one of the key points of the design, by making the voltage source as high as possible. This aids in the speed of response by a large factor and that is much more important in a stepper.
So in conclusion we see applications where L is important and applications where L is not important, but knowing how to deal with it means that gives us the ability to decide when it is important and when it is not, and when it is we know how to handle it. If we ignore it ALL the time, we will eventually run into a problem when it becomes important because we wont know it was important :-)
As in many design settings a good idea is to look at the defining equations as rstofer pointed out. That's the best route to take i believe, maybe the only one that will work in every case.
Just as a quick reference, the inductance enters into the denominator of the motor equation:
K/(s*L+R)
where we also see the resistance R. This is the main torque developer and is powered by the applied voltage minus the back emf. We can see that is similar to a low pass filter, and we know that a low pass filter takes time to react to a step change in input. For the motor that means the torque is delayed by some amount, and that means the force applied to the shaft is delayed by some amount. The amount of delay however is only part of the story, the physical effect, and while the delay is caused by the inductance the purely electrical effect is separate and may appear external to the motor in the leads of the motor as a current and voltage.