Put them in series strings that are as long as you can manage within the constraints of your available supply voltage and the max number of LEDs that should come on in a single group.
Say you have 2V red LEDs running off 5V. With one resistor per LED (chains of length one), the resistor drops 3V and wastes 60% (3/5) of the power. Or if you can put 5 LEDs in series for a total of 10V and run them from a 12V supply, the resistor wastes only 17% of the power (2/12).
Unless they're ultrabright LEDs, 20mA is probably too much. If that's the absolute-max rating, you'll probably find that they're not much dimmer at 5mA. Even if you put 20mA through every LED, that means that a TPIC6B595 (150mA) could continuously drive 7 strings (140mA) of 5 LEDs for a total of 35 LEDs per segment if you use a 12V LED supply!
Edit: deleted all this crap because it basically repeats what CrossRoads said earlier. Ooops.