In an NPN transistor, why doesn't current flow without applying a base voltage?
I suggest that you consider the physical structure of an NPN transistor. It is composed of a pair of PN junctions connected as







simulate this circuit &ndash; Schematic created using CircuitLab

When the base is disconnected, the upper junction is reverse-biased, so very little current flows.

Before you start objecting, you need to be aware that the two diodes are not perfectly isolated, and as soon as current starts flowing in the base-emitter junction, it affects the collector-base junction in such a way as to allow more current to flow. The details require a whole lot more space and math than is appropriate here. 

Nonetheless, the open-base model is accurate at this level of discussion. For a more complete discussion see the Wiki page as a start


  All models are wrong. Some are useful.


Finally, as a nitpick your opening assertion is simply wrong. Some current will flow from emitter to collector, although the amount is usually quite small. The name for this current is the "collector cutoff current", and is normally only of much importance for small-signal transistors.