Does it matter which way you plug stuff into the wall socket
There are two ways to answer this.

No. Voltage is a relative measurement, and in any AC power system (American or European), one voltage oscillates above and then below the voltage of the other. Thus, from the perspective of the appliance, which has connections only to the two prongs of the outlet, it's impossible to tell one from the other, because the system is symmetrical.







simulate this circuit &ndash; Schematic created using CircuitLab

However, yes. There are things in the world besides those two prongs. For example, the Earth. In the US, an electrical outlet really looks something like this:







simulate this circuit

The connection between one half of the outlet and Earth is made near the electrical distribution panel:



Now consider, if someone should touch the half of the outlet connected to Earth, probably nothing bad will happen. However, if he should touch the other half of the outlet, he's likely to get shocked by completing the circuit through some accidental 2nd connection with Earth, or something else touching it (which is about everything).

So although flipping the plug around and inserting it backwards will probably be no problem with regard to the electrical operation of the appliance, it may create a safety hazard by exposing the "hot" half of the outlet, the half not connected to Earth, such that someone might touch it and be shocked.

National regulatory and licensing bodies have different requirements for an appliance to be certified as safe. In particular, the home's wiring can be backwards, or users can force plugs in backwards. Thus, things like double insulation have been developed to render appliances safe even in the presence of a fault like backwards home wiring.