How can I send data to many IC's without using tons of shift registers?
There are other ways,but for a brute force many pin driver solution:

Back at the beginning of time when steam driven IC's were all the vogue there was the awesome MM5450.  40 pin DIP. 34 on/off outputs. 3 pin control. Or the really keen could do it with 1` pin control and some basic RC timing. I was. I did.

Its day has passed. but, fortunately. neither Micrel or Digikey know this.

MM5450 datasheet
In stock Digikey $5.46/1

It's a very benign beat to drive once you get to know it. There is no reset (inless you buy bare dies) so you have to start off getting it synchronised  - it's not hard, just not quite usual. Works well.

For single GPIO pin control the pin acts as data out and clock with some RC timing.
Fot ICs with clock/data/load you can do all 3 with RC timing on one pin. 

And there is a 44 pin PLCC pkg version available.



AND!

SN74LS673 16 bit SR, 24 pins
http://www.ti.com/product/sn74ls673

ICM7243
http://www.ebay.com/itm/ICM7243BIPL-HARRIS-40-Pin-DIP-LED-DISPLAY-DRIVER-ICM7243-7243A-/390402848376

And others
http://www.ebay.tv/sch/i.html?_sop=7&amp;_nkw=led+driver+ic&amp;_frs=1