Safety is the art of not killing yourself. Surprisingly, killing yourself can be bad for your health.
How to Kill Yourself
"Fifteen thousand volts?! 15,000 stinking V? I'll kill myself!"
Not necessarily! It's not the voltage that kills you, it's the current.
Read this page, or at least realize that something as low as 200mA DC can kill you, and something as low as 5mA AC can kill you.
This current will probably have to pass through your heart to kill you. It does not always kill by outright stopping your heart, though--it can also kill by fibrillating it (causing it to go crazily fast instead of at zero speed).
How to Work Without Doing Getting Yourself Killed
At this point, it is assumed you're not suicidal: you'll want to avoid having current pass through your heart, especially if it's AC.
The way I've heard this is usually done is by working with one hand while a circuit is live, and keeping the other hand behind you in your back pocket, not touching anything. You can find a reference to this practice here. This reference does not, however, explain why you should do this.
This 'For Dummies' book claims that it helps avoid putting a current through your heart. The idea is that you're usually grounded via your feet, which are closest to the literal ground in most circumstances. Thus, the fastest path through your body for current will be from the buggy circuit you're working on, through your arm, down your side along the closest leg, and to the ground.
Think about that for a second: if you're working left handed, this may present a problem. If your right foot is elevated from the ground, this may present a problem. If your left shoulder touches some sort of ground (a pipe running along the lab's walls), this may present a problem. Presenting a problem could be defined as your heart stopping.
One hand in your back pocket may be a good rule of thumb, but remember what the reason for that rule of thumb is at all times: you must always stay aware of what the fastest path to ground is, and make sure that your heart is never part of it.
Let's reiterate that a few times:
Never Let Your Circuit Ground Through Your Heart
You must always stay aware of what the fastest path to ground is, and make sure that your heart is never part of it.
If I could repeat that three times, I just might, but I'm afraid I'd lose your attention.
MY BUDDY IS JUST TWITCHING TO SHOW ME HOW AWESOME HIS CIRCUIT IS
Your buddy is shocking himself. It began with a "bzzz" and possibly a yelp.
Usually it ends with a hand being jerked at high velocities. Perhaps a tool sailing humorously across the room, or right into his face. That gash in your lip he just left with the screwdriver? Chuckle, find the first aid kit, and get some gauze: you've just experienced the best-case scenario.
That hole in your buddy's cheek? It might be time to load him into the car and get to an ER, since it looks pretty nasty.
If he's just twitching there, though... you have a major problem. He has clamped up on a circuit, and his muscles are spasming and contracting in such a way that he cannot let go of the source of his impending death. It's also probably AC, since it's much better at causing that spasming and contracting, so it's probably coming much faster.
Either way, you must now find one of two things: you need a way to turn off the power, or to push your buddy away from the circuit without potentially being another ground. Pulling your buddy away is not an option: you will clench on to him in the same way that he is clenching to the circuit. If you see a broomstick or something to push him away, grab it in a hurry and give him a good, hard nudge away from the circuit. If this isn't possible, try to find a way to press the power switch on his power supply--this is often somewhat isolated from the faulty circuit. If it's battery-powered and handheld, try to get the circuit out of their hands using a non-conductive tool, or to break it using a non-conductive tool if that isn't possible.
Whatever the case is: if your buddy cannot get away from the circuit, he is part of it and must be separated without you yourself becoming a part of it.
5 Fun Ways to Hurt Yourself
Several other things to keep in mind, for when you're not wondering why you have your hand in your back pocket (or whether it's actually being effective at right that moment):
Solder gets hot and can splash. It's a nuisance if it splashes on your skin, but you might be one-eyed after a bad encounter. Wear safety glasses while soldering.
A soldering iron is hot. Do not attempt to touch the soldering iron. You will burn yourself.
Do not attempt to hand your soldering iron to your buddy, as he will burn himself. Put it in the stand. He can get it from the stand. That isn't rude, it's courteous and safe.
Do not touch something that you just finished soldering for a couple seconds. The larger it is, the larger the value of "a couple" should be. At some point, you're going to fail to judge this, and it will hopefully only be mildly irritating. Keep in mind, though, that a sufficiently large object will retain a lot of heat over a long time, and that it is possible for it to cause blistering burns many seconds later.
Metal Can Be Sharp
All of those metal things can cut people. The band-aids are in the first aid kit.
Lasers Are Lasers
Don't mess with them--[here's a boring old fact sheet on laser classifications]. Did you notice that laser pointers can damage your eyes, especially if your blink reflex is dulled in any way? (If you've been debugging any sort of light, your blink reflex may be dulled. If you're tired, like when you're in crunch time, your blink reflex may be dulled.) Oh, and those are only some laser pointers. Most will fall under class 3, which will damage your eyes. Don't even think of horsing around with one, in any way: there's a reason most EE labs that do any sort of work with lasers winds up with this sign posted:
Keep in mind that blindness is a career-ending disability, and respect your fellow labmates by never pointing a laser in their general direction.
Don't Mess With CD Players
As a quick side note: the laser in a CD player is class 1 because it's enclosed. The invisible infrared light it emits will blind you, and you'll never even have the fun of seeing it. Don't take apart CD players, and certainly never turn them on unless they're fully reassembled and you've triple-checked that there's absolutely no chance of optical reflections leaking out in any way.
Tools, In MY Body?
We have lots of tools that can cut, stab, impale, destroy, cauterize, blemish, sneeze at, or otherwise interact with your body in negative ways. Point such tools away from your body.
Dremels go side-to-side, so that you never risk having the Dremel fly into your body, or having the workpiece fly into your body.
In general, think about how the tool might move and how the workpiece might move if there's a failure. Don't let the direction ever be "towards myself" or "my peers".