Q:

Why might you choose to change to using an aftermarket throttle body? 

I have heard that some people might want to buy an aftermarket throttle body.  
Is the reason for this simply to replace a broken one or are there also other specific advantages (and disadvantages) to them? 

A:

One of the few reasons to change to an aftermarket throttle body is performance.  The throttle body is a common bottle neck that may restrict air flow.  This restriction comes from one of two places.  

The engine has had upgrades or some kind that allow it to "breath" better.  While the throttle body was not restrictive before the upgrades, now that the engine thirst for more air the throttle body becomes a bottle neck.  
The throttle body was deliberately restricted by the manufacturer.  GM is well known for "de-tuning" their engines.  The Quad-Four was a well known de-tuned engine.  The rumor was that the transmission could not handle the power the engine was putting out.  It was then easier to put a smaller throttle body on the engine than upgrade the transmission.  

A:

In your other question: What is the effect of the throttle body on the power curve produced by the engine?,  I answered the question of what a throttle body (TB) is and it's basic operation.  In the answer, I talked generally about how the function of the TB.  I point others there so they have a basic knowledge. 
Back to this question:
There are two main reasons why someone would want to replace a TB:

Function - The current one is broken and needs replaced.  A typical scenario I've seen in this situation is the bushings which the throttle plate rod rides on will get worn out.  This can allow un-metered air to get into the intake an cause problems with the how the engine runs.  Replacement in this case would most likely be back to a stock one. 
Performance - You want more giddyup!  If someone wants to improve the performance of their vehicle, a bigger TB would allow more air to be brought into the engine, which could potentially make more power.  

An engine is basically an air pump.  You bring air into the engine (through the intake system and throttle body), it get's mixed with fuel, it all gets burned and becomes exhaust, and gets sent out through the exhaust system.  As I've stated before, the TB is one part of this air pump system.  It is a restriction in this system.  It also regulates the amount of air which can enter.  Having a larger TB on there will give the engine the potential to use more air, but only if the engine can use it in the first place.  
If you put a larger TB on the engine without making adjustments to the other parts of the engine which also affects air flow, it will only be a waste of money.  To properly use the bigger TB, you need to adjust valve events (most likely through changing out the cam shaft), enlarging/smoothing the intake/exhaust ports (through machining and porting), and a hi-flow exhaust system.  Only then does the true potential of an aftermarket TB make a real difference.  Then again, you'll want to make sure the bottom end of the engine can handle the new found air flow. 