Electronic – 1 Device, 2 Power sources

Yes, this is simple. It can be done passively with two diodes. At these low voltages, they can be Schottky diodes, thereby dropping less voltage and being more efficient.

Put a diode from each source to a internal power node. When 12 V is present, the internal power node will be at just under 12 V. The diode to the 7.2 V source is therefore reverse biased, essentially disconnecting the 7.2 V source. When the 12 V source goes away, the internal power node will be at just under the 7.2 V.

A switching power supply can deal with this variation in source voltage and still produce your final intended 5 V reasonably efficiently regardless of which source is providing the power.

If voltage drop is not an issue you can just tie all the power inputs together with diodes: all the cathodes are connected together, and that's where you power your circuit from, and you hook one power supply per each anode. Issues? Voltage drop, power dissipation. That can't work for big boards where much current is needed. You can use Schottky diodes to achieve a lower drop but that pretty much is it.

If there's a some sort of precedence between the supplies you can sort of solve the problem still using only diodes. Here's a sketch:

^{simulate this circuit – Schematic created using CircuitLab}

If PS1,2,3 are rated the same voltage then PS3 is the highest priority one, i.e. when it's on that's what's powering your circuit. If PS2 kicks in D2 is off since the voltage drop across it is 0V, but if PS3 fades away then your circuit is powered through D2. Note that when you are using PS1 you have two diodes drop to take in account.