Operating a Switched Mode Power Supply without a Load
It's difficult to generalize this sort of behaviour. Some power supplies will work at less than the minimum load but with degraded performance. Other power supplies may shut down, and others still may malfunction  badly (oscillate / shut down). Others may behave perfectly.

Quite often, basic power supplies use pulse-width-modulated (PWM) toplogies with inductive storage elements. The switching frequency is fixed and duty cycle is varied to control the output voltage as a function of load and input.

When the current in the inductive storage element never goes to zero, the converter operates in two states - switch on and switch off. This is called continuous conduction mode (CCM). Once CCM is achieved, the duty cycle essentially doesn't vary (unless the input changes) - the converter behaviour doesn't change with load and things are fairly consistent.

At very light load, there isn't a DC current level in the inductive storage element. The converter now has three states of operation - switch on, switch off and inductor current decreasing, switch off and inductor current = 0. This is called discontinuous conduction mode (DCM). In DCM, output load affects the duty cycle as well as input variations. 

Most controllers have a minimum PWM on-time that can be achieved - if the plant tries to command a duty cycle lower than this minimum, you may see erratic output, missing pulses, high ripple current, etc. - some converters will simply stop regulating (the output will rise). Some controllers detect this and go into controlled burst mode to keep the output loosely regulated.

Also, the feedback loop compensation will be dictated by the CCM performance of the converter, since there are nasty things (like right-half-plane zero) in CCM that need to be stabilized that essentially aren't there in DCM - the compensation may be sub-optimal and things like transient response will be affected.