Teckel, I've received a Due and downloaded NewPing (you asked earlier in the thread). The immediate issues are that it includes "avr/io.h" and "avr/interrupt.h", neither of which seem to have obvious counterparts for the ARM due.
With those headers missing, the following lines become issues:
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp: In constructor 'NewPing::NewPing(uint8_t, uint8_t, int)':
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:19: error: cannot convert 'volatile RwReg*' to 'volatile uint8_t*' in assignment
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:20: error: cannot convert 'volatile RoReg*' to 'volatile uint8_t*' in assignment
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:22: error: 'portModeRegister' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp: In static member function 'static void NewPing::timer_us(unsigned int, void (*)())':
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:151: error: 'OCR2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:152: error: 'TIMSK2' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:152: error: 'OCIE2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp: In static member function 'static void NewPing::timer_ms(long unsigned int, void (*)())':
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:167: error: 'OCR2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:168: error: 'TIMSK2' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:168: error: 'OCIE2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp: In static member function 'static void NewPing::timer_stop()':
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:177: error: 'TIMSK2' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:177: error: 'OCIE2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp: In static member function 'static void NewPing::timer_setup()':
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:195: error: 'ASSR' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:195: error: 'AS2' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:196: error: 'TCCR2A' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:196: error: 'WGM21' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:197: error: 'TCCR2B' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:197: error: 'CS22' was not declared in this scope
C:\arduino-1.5.1r2\hardware\arduino\sam\libraries\NewPing\NewPing.cpp:198: error: 'TCNT2' was not declared in this scope