I'm sorry this is an ignorant question. I am working on hooking up leds for my raspberry pi. I keep hearing about mains power and how dangerous it is. I'm using a 5v adapter that is plugged into an outlet. If something goes wrong and I get shocked will I be okay? This might be a really stupid question, but I figured I would be better safe than sorry.
As long as you are using an approved consumer power supply (such UL, TUV etc depending on your locale in the world) it is designed such you are not normally exposed to any hazards. This assumes you don't do anything foolish such open it's sealed enclosure or dunk it in water.
So - no the 5V cord coming out of it should pose no risk to you. Voltages below 48V are not considered hazardous to humans.
But don't stick any wires into an AC wall outlet.
Short answer is: its possible.
There is a famous case about a woman who died after answering her phone. Reportedly it was a fake chargers fault.
Take a look at this article reviewing different chargers.
Note that many cheap chargers do not respect regulations and recommendations needed for safety certification.
If you take the right precautions and use decent gear you will be much safer though and shouldnt worry.
The adaptor is supposed to be insulated to prevent this, even in the case of internal failure. The only circumstance it could go wrong is if it's an illegally sold one with false CE/UL certification.