Emf interference on arduino and breadboard , using 74HC595 shift register, how to prevent it?
This is either a decoupling problem, or an unconnected wire. As the commenters have said, you'll need to add some capacitors. Fit them as physically close as possible to the 74HC595's power pins (your diagram shows it too far away). Try at least a 0.1uF ceramic capacitor as well as the 100uF electrolytic. Try as much as a 1uF ceramic.

The other possibility is an unconnected pin. CMOS parts can be affected by electric fields when there are unconnected input pins. Have you connected all the unused input pins to either Vcc or Ground? Are you sure that the breadboard wires really are making contact? Solderless breadboards are notorious for unreliable contacts.