I've experienced Cinnamon on Linux Mint crashing (leaving the display frozen), but it was possible to go do a tty with ctrl+alt+functionkey (each of f1-f6 goes to a different tty, f7 goes back to the display) and manually restart it. But this hasn't happened to me in the last couple months, so it's probably fixed.

Then I've had some full freezes where precisely nothing at all works, but those happen very rarely and I wouldn't be surprised if that's a hardware problem.

Then there's full RAM. Yes, linux still hasn't figured out how to not flop on its head dead when RAM fills up; though usually the mouse pointer isn't immediately frozen.

> I didn't know how to even start troubleshooting a thing like that

Reading the system logs is always a good place to start.