Can the MAX7219 driver 16 individual LEDs?

I've used the MAX7219 before with an 8x8 matrix but I'm wondering if it can also driver 16 individual LED that are all common grounded? No multiplexing or PWM just being able to control 16 leds.
If that's not possible what other easy to use LED driver ICs are there I should look at?

I'm not sure it will. However, you could use pretty much any shift register if your LEDs are all common-grounded. They're cheap, easy to wire, and very easy to interface to.

Adafruit have a tutorial for Arduino here: https://learn.adafruit.com/adafruit-arduino-lesson-4-eight-leds/overview

Same thing with Espruino really - but you can just chain most shift registers together, so you can add as many blocks on LEDs as you want.

Is it safe to use the 595 to run 8 LEDs at once? I think I remember reading somewhere you shouldn't do that as the current it too high for the IC but I could be wrong?
I'm a complete noob at electrictronics and still learning.
PS.where is a good place to learn/find out about ICs?

I'm not sure, but I doubt Adafruit's example would be doing bad things to the 595. They're usually quite good about that - if you used maybe 1k resistors instead then the current drawn would be tiny and would definitely be fine though.

Maybe others might be some help here - but Adafruit is a actually pretty good source for these kind of tutorials I think. Also there are loads of resources for Arduino if you search, and converting the software (at least in these cases) for Espruino is trivial.

595 is rated for only 70mA max.

So depends on how much current you feed the LEDs - as long as it's under ~9mA you should be okay. With Vcc=5v, a red LED (~2V drop) could have a resistor as small as 330 ohm on it, but no less, assuming you're going to have eight of them on the shift register.

Here's an example that does what you ask... https://hackaday.com/2011/11/05/controlling-shift-registers-via-spi/

Is it safe ...
Depends on a few things. Do you expect all LEDs to be on at same time or more of a sparse display? You need to limit power disipation of the 595, which depends on the package type. Newer SM LEDs usually don't require as much current, which also varies by color, that can help lower power.