Why do tropical cyclones not tear themselves apart? A tropical cyclone is the generic term for a hurricane, typhoon, or tropical storm.  Tropical cyclones derive their energy from evaporation of water at the ocean surface which ultimately recondenses when it cools to the saturation point.  The rotation of a tropical cyclone is caused by the Coriolis effect.  
What is unclear to me is: Why do these massive bodies of warm, moist air clump together over thousands of kilometers?  What physical process causes them to be drawn in towards the center of the storm?

*image taken from the Wikipedia article on tropical cyclones
 A: The rotation is part of the key to the storm itself.  Primarily the pressure and temperature differences are what causes these systems to take the shape and forms that they do.
Once a tropical depression starts to form you can already see rotation in the moisture around the low pressure zone, even through it typically looks nothing like a hurricane.  Not until the depression deepens and reaches tropical storm status does it tend to group together in a circular fashion around the low pressure zone.
This is stable because of the evaporation and condensation that rises and falls around the edge of the wall.  The Coriolis effect causes additional mixing of these layers and encourages the evaporation/condensation cycle that drives these storms.  Without the rotation they tend to be just turbulent air masses around the low.  Notice the rotation feeds the inflow and outflow of the temperature driven winds.

Likewise a cross section reveals the relationship between the wind and pressure zones around the core of a tropical revolving storm.

Without the rotation the transport of hot water vapor to the colder higher levels is much slower and thus less wind, less condensation and less of a storm is generated.
(Images taken from a short article about how these storms are fueled.)
A: Water vapor is less dense than dry air.  In a rotating system, moist air would be forced inward and dry air outward.  
A: Due to pressure gradient. The center is a low pressure region.
