Here's a nice little walkthrough for when you should call the cops:

Severe Injury/medical emergency -> No, you should call an ambulance.

Car Crash -> Fire department and ambulance

Mental Health Crisis -> Community healthcare network. 211 in most communities, or find a local community group dedicated to that care

Fender Bender -> Get yourself to a collision centre. They don't give a shit.

Crimes -> You can try the non-emergency line, but they're not gonna show up or even call back. Enjoy being on hold for 3 hours.

Someone who's an active danger to the public -> That is the cop.

There's no reason to call the cops, or for them to exist in the first place.

@mayintoronto Ontario collision centre is staffed by cops for no real reason... In Quebec you used to just fill out a form with the other parties, no cops needed.
@va2lam I'm a big fan of parking tickets, and not even the cops consider parking enforcement cops. (pretty sure they're not armed.) They're in the grey area.