Now that weed has been legalized in Canada, what would happen (from a legal perspective) if you tried crossing into Canada by car from the US, with Cannabis products?
You'd be committing a crime, and could be punished severely.
You can find the full text of the Cannabis Act here. (As DJClayworth mentioned, it does not come into effect until October 17, 2018.)
If you are crossing into Canada with marijuana then you are importing it, and importation will (continue to) be illegal under the new law. It is punishable by up to 14 years in prison. See Section 11 of the Act.
The government will be able to issue permits for importation, but only for medical or scientific purposes, or for industrial hemp. See Section 62. You couldn't get a permit to import your recreational weed. Even if your weed is for your personal medical use, I expect that getting a permit will be a complicated process, intended for large organizations only.
How the law will actually be enforced is something we don't know yet. It's possible that attempted importation, on a personal scale, won't be punished so severely, or that they will just confiscate the drugs and give people a warning. But it's also possible that they'll enforce it strictly and impose long prison terms. In any case, it certainly won't be legal, and you can't expect anything good to come of trying it.
First important point marijuana has not yet been legalized in Canada. It is not legalized until 17 October 2018. People can and will be prosecuted for possession until then. (If your marijuana is for medical purposes that's a different matter, but you would need to prove that).
You should also note that the sale and distribution of marijuana will still be regulated. Exact rules are up to the province, but in all cases selling without an appropriate license will be illegal. I can imagine that if you were found with an amount of marijuana that implied you were selling it you might be prosecuted, but nobody has tested the laws in this area yet.
Nate Eldredge has corrected me that importation of marijuana will continue to be illegal and potentially heavily punished. I personally can think of no good reason for importing anything from a place where it is illegal to where it is cheaply and legally available. The intention is to make legal sales no more expensive than the previous illegal price.