Tap-tap-p-p-p all the way round the centre? Masculine single smash against the side of the bowl? Use an implement of some kind? None work for me - I always get showers of shell into whatever I’m cooking. So what’s the secret?
Give it a good rap on the edge of the bowl/pan so that there is a real opening to use to pry the shell apart. In my experience, shell get in the bowl when you have to push your fingers into the opening. Another old cooking trick is to break each egg separately into a small bowl first. That way if one is a disaster, you don’t ruin your whole recipe. (This mainly applies to separating egg whites, but could be useful for you, too.)
Give it a whack with a butter knife. The egg should crack cleanly.
No, somewhere between the two. Start with a nice sharp rap on the edge of the bowl or something hard but not flat. If that’s not enough to let you open the shell, give it one more rap adjacent to the cracked area. If you still get shell in the bowl, find eggs from chickens that have more glue in their diet. 
I actually find it easier to do this with one hand than with two. Cradle the egg nicely in your palm. The “equator,” and cracking point, will be between your 2nd and 3rd fingers. When the shell is cracked, pull the thumb/1st finger/2nd finger end away from the 4th finger/5th finger end. The eggs drops into the bowl, the shell is still held in your hand.
Forget the rim of the bowl, crack it on the flat surface of the counter. This leaves the shell in larger, more manageable pieces. If you’re feeling really suave, open the shell with one hand.
Flat surface all the way like Krokodil says, especially if you want to separate the whites and yolk.
I always do it like this:
Hold the egg in one hand and smash it with medium velocity against the edge of the bowl, cup, etc. such that the edge of the receptacle is pushed about halfway into the egg. Then quickly pull the egg up and move it over said receptacle, pulling the shell apart with your fingers as you do. The egg will slide cleanly out of its shell, and you’ll look really cool by cracking it with one hand.
Hamsters ate my post on this, but yeah, this works the best and is the way I see chefs do it.
For separating, break the entire egg carefully into a bowl, then remove the yolk from the bowl with your fingers, allowing the whites to escape. This works especially well if you are separating many eggs. Beats the heck out of the shell-to-shell method.
Smashing against the edge of the bowl pushes shell fragments into the egg. A flat surface is the way to go. Then, pull apart as described above.
I follow the Alton Brown method of cracking the egg on a small plate. The advantages of cracking on a flat surface, as Krokodil says, but you don’t have to clean egg white off your counter. Just wash the plate when you’re done. AB says that cracking on the rim on something drives shell fragments up into the egg, along with whatever germs might be on them. Makes sense to me. Although Mr. Purl is hopelessly unable to master the flat surface cracking.
Nice to see that everybody is avoiding having this thread moved to GD or the Pit by delicately avoiding the insoluble “Big End vs. Little End” argument.
Just a note… the cracking into a seperate dish is not so much to prevent shells from getting in (though it helps with that) but in case you get a rotten egg so you don’t drop it in with all the others and have to toss out a lot of good eggs because the rotten one was dumped in.
I have not seen anyone here use the “one egg to crack open another egg” method.
Take the egg you intend to crack open in your left hand. Take another egg in your right hand and hold it so that the small end is pointing outward from your fingers. Quickly hit the small end of the egg in your right hand into the center of the egg in your left. The physics of this situation will have the egg in the left hand crack open and the egg in your right hand remain unharmed.
I use this method if I don’t have anything clean to break the egg on (which in my house is very often!)
I’m a one-handed cracker. I find it easier to rap the egg on the edge of the bowl and separate the two sides with one hand. Mr. Ruby calls me a showoff. 
One-two-three Crack.
Or did you never see the original version of Sabrina, with Humphrey Bogart and Audrey Hepburn?
Seriously though, I just rap the egg a couple of times against the edge of a bowl, and then open the egg with one hand. I usually scramble the eggs, so I don’t have to worry about whether the yolk breaks.
War injury?
Maybe the problem is that you’re…a GorillaMan.
I prefer the one-handed, suavity-suave, flat surface method.
But which two of my thumbs do I prise the shell open with?!?!?