Another approach is to use FET switches. For example, if your chip uses 5V and 3.3V, and wants the 5V first, then you put a FET on the 3.3V wire, and you use a comparator (or power-good signal, or some other means) to determine that your 5V is O.K., and only then you turn ON your FET.
The disatvantage over using diodes is that it is more complex, and some times costs more. The advantage is that the power dissipated in the FET is small (especially when something goes wrong with one of the supplies), compared to the solution with the diode, and hence the solution may be smaller and more reliable.