Should I ground my case
I think a good starting answer is

(1) -  It would stop the case from becoming live if something shorted to the case would it not?  :-)

(2) BUT, not only stop it becoming live, but also provide the intended means of operating the provided protection equipment if a phase to case fault occurred.
 aka "blowing the fuse" or "tripping the breaker" as the case may be. 

The operation of fuse or breaker in the case of a fault is probably more important than keeping the case from reaching mains voltage at all. Both achieve much the same result in terms of case potential above ground BUT breaker/fuse tripping both tells you there is something wrong and removes a potentially lethal problem which may otherwise manifest in some different manner.

(3) Along the way it may stop nuisance shocks which occur from current through any X and Y caps that may be fitted (probably none in your power supply). 

Also ground referencing your supply stops the whole assembly wandering off to a semi-random voltage of it's choice relative to ground that has nothing to do with the power supply proper. eg in some cases an ungrounded case may be driven by electrostatic charge from the effect of carpet on clothes etc  and gain a voltage of thousands of volts (very literally) relative to ground. Touc it when grounded and you may feel a small or not so small kick as the stored energy "discharges". What feels small to you may be the last thing that your circuitry ever "feels".