Interrupts on Arduino Due
Quite simply, it's because the microcontroller that the Due uses (AT91SAM; datasheet PDF) supports it:


  Up to 103 I/O lines with external interrupt capability (edge or level
  sensitivity), debouncing, glitch filtering and on-die Series Resistor
  Termination


To the second question, yes, there are plenty of MCUs that have this same feature. For example, you can use the Atmel parts selector to find MCUs whose # of IO pins == # of external interrupts.