If Hitler had been captured by the Allies alive, would he have been executed and when?

[Frodo]

I assuming you mean the Soviets, since they were the ones designated Berlin as their prize early on.  

I think Stalin would probably have had Hitler marched through the streets of Moscow before being sent to one of the more notorious gulags where we would likely have never heard from him ever again.  A hanging or a bullet to the back of the head would probably have been deemed too clean a death for Hitler.  

Hitler committed suicide for a very good reason.  He knew Stalin took his betrayal of that 1939 pact personally, and probably had something very 'special' planned for him if he were ever taken alive.  He would have counted himself fortunate if Stalin handed him over to the Nuremberg Tribunal instead.