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?
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:
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.
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.