There are many aspects to this, and the question requires a more in-depth answer than can be given here. The distinction between married and common-law couples impacts many areas of the law, including Estates, CPP entitlement, Survivor Pensions, etc, and often hinges on the specific facts of your scenario.
But to answer from an Estates standpoint: If you are legally married, and your spouse dies, then there are certain legal rights that arise whether there is a will or not. These same rights do not accrue to you if you were in a common law partnership with the deceased person at the time of his or her death.
Under Ontario law, if your common law partner has died leaving a Will that specifies you to receive certain assets from the Estate, then you do have an entitlement accord to those instructions. In narrow circumstances you might also be able to bring a dependency claim, if a court concludes that your partner did not adequately provide for you in the Will.
But if your common law spouse dies without a Will (i.e. intestate), then you would not inherit any part of his or her Estate. In those circumstances you may be able to bring a legal claim against the Estate for unjust enrichment, but again this will not be a common scenario.
If you have specific questions around other aspects such as CPP and Survivor benefits, it is necessary to consult your lawyer for specific advice that pertains to your situation.