Current limit?

I was reading the "A Complete Beginners Guide to the Arduino" and I was wondering how many 74HC595 chips you can daisy chain. Lets say you wanted to hook up 24 leds running at 15 milliamps will it be able to handle the load. How about 32? The author said on page 87 that you can hook up 6 chips, however I think each one was using its own 3 inputs and not daisy chained. Thank You

When you daisy chain these chips, they still require individual +5V/GND connections. The current limit of each individual chip is not changed and can be found in the datasheet. If I remember right, it is about 70mA total for a 74HC595.

If you need more, try TPIC6A595, TPIC6B595 or TPIC6C595. These essentially provide similar function, but with a lot more current capacity (only current sink, open collector).