Inductive kickback protection?
Kinda, sort of, but not really. I'll look at the A4988 (datasheet).

The motor pins are connected by diodes to ground and Vbb (the motor suppply voltage). Essentially, they act as a bridge rectifier making any back EMF or inductive spikes appear (rectified) on Vbb. If you were to suddenly power down the driver this could cause a rather large spike on Vbb.

According to the datasheet, there is a 40&nbsp;V Zener on Vbb which will clamp the voltage to that level. (Another popular stepper driver, the DRV8825, does not appear to have this Zener - always check your datasheet!)

So, yes, there is inductive kickback protection. However, it only clamps the voltage to 40&nbsp;V. Depending on the rest of your circuit, this could be quite damaging.

The datasheet recommends that a 100&nbsp;&mu;F capacitor be placed on Vbb. If you are driving a typical stepper motor with 2&nbsp;A and 4&nbsp;mH coil inductance, the energy stored in the coil is 8&nbsp;mJ. This energy is only enough to take the capacitor up from 12&nbsp;V to ~17.5&nbsp;V, so if you have a large enough capacitor on your stepper driver (as you should!) then you're protected against inductive kickback.

Note that if you move the motors by hand then you can still build up a higher voltage on Vbb. I've heard anecdotes of people who damaged their printers like that.