Which are the unused digital pins after L293D motor shield is installed on a Arduino Uno board?
If this is the same board as seen on Banggood Which may also be seen at Adafruit
The schematic shows most of the digital pins in use
D3  - PWM2B  
D4  - DIR_CLK  
D5  - PWM0B  
D6  - PWM0A  
D7  - DIR_EN  
D8  - DIR_SER  
D9  - PWM1A  
D10 - PWM1B  
D11 - PWM2A  
D12 - DIR_LATCH

The analogue pins A0-A5 are still free - these can be used as digital pins.