Ok thank you so much. Why is that dangerous? Im curious about.
Althought there's ~5VDC between the Arduino's ground and Vcc, the Arduino's ground can end-up at about 170V* relative to earth ground and that can kill you.
Be smart and use a step-down transformer (which provides 100% electrical isolation from the power line) or buy power supply (which will be isolated).
P.S.
Plus, a brute-force Zener regulator is a lousy and inefficient power supply design!!!!
*120VAC RMS is about 170V peak.