Why don't most non-East Asian varieties of rice stick together?
Please see the excerpt below from  this page . There is also a chart that lists different types of long, medium, and short grain rices and their characteristics and usage examples.


  Rice is composed of two different types of starch molecules: amylose and amylopectin. The amounts of these two starches determine the texture of rice when it is cooked.
  
  Rice with higher amylose content, such as long grain rice, is firmer and fluffier. Rice with lower amylose content, such as short and medium grain rice, has a softer, stickier texture.
  
  The Effect of Starch on Rice Cooking:
  
  
  Dishes such as risotto and sushi rely on rice that is low in amylose to create their characteristic soft and sticky textures.
  Rice dishes that have fluffy separate grains, like rice pilaf, are best made with rice that is higher in amylose starch.
  Some sticky rice dishes, like many Asian desserts, are made from varieties of rice that contain no amylose starch. These varieties of rice are called sweet, waxy or glutinous rice.
  


In general, the shorter the grain, the stickier the rice will be.