What keeps the kickback voltage from reaching an infinite voltage?
A real inductor looks like this (shown below is an inductor with 4 coils) there is a small amount (usually in the pF-fF range) of capacitance between each coil. Each piece of wire also has some resistance associate with it. 

Because each coil in an inductor has resistance (or each section of wire if you consider one coil) this impedes the current and reduces the voltage. The small amount of capacitance will also store some of the voltage and prevent an instantaneous change in voltage. 

These all soak up energy that prevents the Electro Motive Force (EMF) that has been stored around an inductor from generating an infinite voltage. An inductor can actually be simplified into a circuit such as the one to the left below.







simulate this circuit &ndash; Schematic created using CircuitLab

A superconducting coil would be able to generate much more massive voltages because of much lower losses due to parasitics.