There are literally hundreds of parts and engine components that can cause a car to stall when accelerating. However, there are some known culprits that are more likely than others to cause this problem.
Fuel System Components
A car's fuel system is made up of many components, any of which may cause a car to stall under acceleration. For example, fuel filters may become clogged due to low grade fuel, fuel pumps may stop working or fuel injectors may not be delivering the correct ratio of fuel to power the car while accelerating.
Exhaust and Emissions Components
Dirty and/or clogged emissions components can also cause a car to stall during acceleration. If filtering components and sensors are not functioning as they should, byproducts from unburned fuel--or low grade fuel--could accumulate, resulting in air not being able to circulate through the system.
Shorts in wiring are other common reasons why a car may stall while accelerating. Since most newer cars rely heavily on their engine's computerised systems to function, there is a significant amount of current flowing through the vehicle at all times to power the system. Loose connections on engine parts can have the same effect as well as burnt and/or worn electrical connectors.