Pedants only past this point:
It's not really clamping the voltage spike, its providing a path for the current to continue flowing (an inductor is a bit like a constant current source with unlimited voltage compliance). There is simply no voltage spike when the diode is there, its the lack of a current path that 'generates' the voltage spike because the inductor continues to push electrons round the circuit at the same rate.
When the diode is there the current will take a lot longer to die down, so the spike becomes a pulse of much longer duration, an effect that isn't really explained by 'clamping'.
An analogy: with the diode its a bit like stopping a runaway lorry with a gravel-trap. Without the diode the lorry hits a concrete barrier when the switch opens. Substitute velocity for current, force for voltage and mass for inductance. The forward-voltage drop of the diode plus the IR voltage in the coil provide a small stopping voltage (force), so things slow down smoothly. With no current path the road ends in a concrete wall and the stopping voltage/force is extremely large. If you want to extend the analogy then the IR voltage drop across the winding is the lorry's rolling resistance, and the supply voltage is like the engine's driving force (which normally balances the rolling resistance).
Thus when switching on there is no big spike since all that happens is the engine starts and the lorry pulls away smoothly. If the fuel runs out that's like the supply voltage falling to zero (not the same as switching the transistor off as current can continue to flow). Opening the circuit is like the road suddenly ending in a barrier (in fact the barrier is the transistor, and if its not strong enough it gets damaged in the crash).
When there is no inductor it's like having a massless lorry (lets say its an inflatable lorry!) - it's easy and safe to stop with a barrier since there's no real momentum to dissipate.