The Yukon, Alberta, Ontario, New Brunswick, Nova Scotia, Prince Edward Island and Newfoundland do not have no fault insurance.  All of these provinces have private insurance companies that compete against each other for customers.  All of these provinces have restrictions or “caps” on compensation for less serious injuries but you can still sue at-fault drivers for damages and if you think the insurance company is treating you unfairly, you can sue in court and have your case decided by the court. None of these provinces force you to appeal to a non-arm’s length tribunal that is hired and fired by the government.
While Quebec has private insurers, it also has a no fault insurance scheme which is unique in Canada because of its system of civil justice, unlike the rest of Canada’s common law jurisdictions.
The only other no fault jurisdictions in Canada are Saskatchewan and Manitoba, both of which, like B.C., have government-run monopolized auto-insurers with no insurance market competition.  However, in Saskatchewan, individuals are given the choice to buy their own insurance to recover full damages for all their harms and losses. In B.C., no fault insurance is mandatory for everyone with no choice option.