tiggerpurrrz,
As far as despatch and in-flight is concerned, the APU is a source of AC power along with each engine driven generator. It is a requirement that at least two source of AC power are available. With most twin engines aircraft, if the APU is inop and an engine driven generator fails in-flight then there is only one source of AC power remaining. It is a requirement to divert to the nearest suitable (suitable = performance, facilities and weather) airport.
For most twin engined aircraft with an APU inop on a standard short haul operation with nearby enroute alternates available, it is perfectly safe to depart and perfectly legal. For an oceanic/ETOPs flight it is not safe and I would have thought not legal.