OllyR:
but the interwebs suggests (in places) that I could burn out the chips if I run all the LEDs on one row at the same time for example. In other places people report doing it with no issues.
can I? or a more productive question, how do i work it out?#
The 595 can take about 20mA per pin, but only about 70mA for the entire chip.
ie. You can do 20mA on three pins, 10mA on seven pins, etc., so long as the sum of all pins is less than 70mA.
If you to run 8 LEDs simultaneously you have to limit them to 8.75mA each (or less).
If you want more current you'll have to add external transistors to drive them or use a different chip. LEDs are tricky beasts to light up properly so your best bet is to get chips which are designed to drive them, eg. TLC5916, TLC5925, etc. The other massive advantage of using driver chips for displays is that you have a much better chance of getting all the LEDs to be the same brightness than if you're using current-limiting resistors.
There's one other possibility but it's a bit horrible: Stack one 595 on top of another and solder all the legs together. You'll get a 'chip' which can handle twice the current. You can run your LEDs at 16mA and stay within the limits.