I have seen many attempts to remove broken keys, but usually without success.
People have used such items as scisors, super glue, blue tack, paper clip,
knife, and many more weird objects. While you might get lucky and flick it out,
the odds are you will push the piece of broken key furthur into the lock
making it harder to remove.
Below is a simple drawing of a broken key in a lock. The red lines represent the
wafers inside the lock (Sorry for the bad drawing). The problem with most broken
key removals is that the broken key can not just be pulled out. This is because
it is stuck behind the front wafer(s). The front wafers will spring back into
their normal locked position making the broken key trapped inside the lock.

In the next drawing the blue objects represent the tools used to remove the key.
The Top and bottom tool are used to hold the wafers up out of the way. The
middle tool is used to grab the broken key and pull it out, past the front
wafers.

This is a simple
representation, but there are many factors that make removing a broken key
difficult. Not all locks have a short front barrel. Many car and motor bike
Ignition locks use a Long neck on the barrel. This makes it more difficult to
see and determine how the key is broken off. Modern Honda and Yamaha motor bikes
are well known for this type of ignition lock.
If the tip of the key breaks off, then it can lodge deep down in the lock at an
angle. When this happens the tip does not want to slide out of the lock because
it can not move along the grooves or warding inside the lock.
There are also other obstacles inside a lock. Most door locks have a dust cover,
which must be pushed in to even see the broken key. Ignition locks have
different configurations of steering lock pins, these have to be depressed or
released for the key to slide out.
When removing stuborn broken keys you need patience and skill to be able to get
them into the correct position and have everything inside the lock correct for
the key to be removed. Not all broken keys can be removed through the front of
the lock. Sometimes the lock has to be dismantled in order to remove the key,
although this is usually in a minimal number of cases.
I would reccomend calling a professional to remove a broken key, due to the fact
that in many cases you will make the key harder to remove by trying to remove it
yourself. If you really want to give it a go yourself, you can make a tool out
of a hacksaw blade. Grind the blade so that you have the teeth and a thin piece
of blade about 10mm - 20mm long. This can be used to go inside the lock and
hook the broken key out.
If you have broken the key inside an ignition lock, do
not drive the car, even if it will start. The broken part of the key may not be
in contact with the steering lock release pin. This may cause the steering lock
to activate while you are driving the car!