The typical approach to interrupt the flow through a circuit is interrupt it at a single location as in the left image.
Do any power loads require both power lines disconnected by the switch as in the right image?
Does AC/DC matter? And in the case of DC, does +/0 vs +/- power matter?
If so, why?
The American, residential, split-phase power distribution system has 240 V across two live lines and 120 V between each line and neutral.
In this system , a single pole switch is sufficient for 120 V loads with only one line being live and the other neutral.
However, a two-pole switch is required for 240 V loads with both both the lines being live.
The following three-phase system example also shows the requirement of a two-pole switch for 208 V loads connected between two live lines.
Incidentally, a three-pole switch is a must to switch 3-phase loads with all three lines being live.
While there may be regulatory or safety reasons you would want to switch both power rails, there is no functional or physical reason it would ever be required. The electrons need to go through a complete circuit, and breaking that complete circuit in even just one place is enough to stop them from moving.
Note that there may be more than one complete circuit involved in a device and in general all of those circuits must be opened, e.g. a three-phase device with three input rails needs at least two of the lines switched off to fully remove power.
More insidiously, sometimes a complex IC can be accidentally powered through its inputs, via the protection diodes intended to stop ESD damage. This is one reason it's usually recommended to switch off the positive supply rather than the ground for digital chips--or to use a built-in disable function rather than switching the power supply at all.
You have to consider the purpose of the switch (including any reasonably foreseeable misuse/misunderstandings) and the characteristics of the supply.
In general there are two reasons to disconnect all of the lines feeding a device rather than disconnecting all but one* of the lines.
* Some devices have more than two lines feeding them. For example a 3 phase motor.
Some connectors of electrical system in Europe is unpolarized - line and neutral are connected at random. As a consequence of the potential uncertainty on which connection is live or neutral many models of power entry modules have DPST switches disconnecting both conductors of the entry lead from the load.
A typical power inlet module (Schaffner FN9280) is an example of a circuit where both power lines disconnected by the switch.
Image source: Schaffner - FN9280
Image source: Schaffner - FN9280 datasheet
I travelled a lot installing equipment so had to get used to all manner of supplies. There is a lot of variation, none of it unsafe BUT!
This is catch all:
Use switches that disconnect all wires. all domestic cables have a neutral so in theory that does not need switching but don't chance it! Someone may have crossed the live phase with the earth. Cable colours vary from country to country so don't chance that either. Ask! There are also some odd ones like 120/120v out of phase to make 240v. That must be dual switched. Biochemistry labs can be a nightmare - especially in the USSR.
Always carry a DVM and a test screwdriver
You asked if a load required a double-pole single-throw disconnect?
You betcha. My 220v air compressor, which uses a 220v motor (two magnetic windings, one for each phase) to drive compression. It requires (and uses) a DPST switch because leaving one hot line active, the unit would try it's darndest to fill itself with air when the tank pressure fell below the pressure-switch cut-in pressure. That would quickly damage the motor — if the motor would turn at all. (If it didn't, the active magnetic windings would rapidly burn themselves out. If it did, the stress of driving a compressor expecting both active windings would also burn it out, just a bit more slowly.)
It's worth mentioning that a great many appliances that require 220v service simply don't require switching. Ovens, stoves, furnaces, air conditioners... But, then again, they're all DPST switched at the breaker box, so I suppose you could say all 220v loads must be DPST switched.
