Yes, you will need 180 to 220 ohm current limit resistors, 1 for each segment.
You will need 100nF caps, one for each shift register's Vcc pin.
You will need a ULN2003 to buffer the common cathode signals - each cathode will have up to 160mA flowing thru it if all 8 segments are on.
The shift register, or arduino pin, will source current into the anode segments, the ULN2003 will sink current.