As was pointed out before, under the landlord tennant act they are not supposed to discriminate if you have a dog, but they will find some other excuse to not rent to you if they want to.
Also, if your pet (any pet) is being a nuisance and causing other tennants to not be able to enjoy quiet enjoyment, well then you and/or your pet will have to go.
When it comes to condos, that is another story all together. Because they have their own set of regulations, they can actually set their own by-laws when it comes to dogs, and many of them have a size restrection, ie. max dog size of 35 Lb.
I am sure that if you search you will find a place that is suitable. I think your best bet is to find a multi-unit house, and have lots of info to prove that you are a responsible dog owner.
One more thing, Landlords aer not allowed to collect a "secuity deposit" in Ontario or any other "pet damages deposit". Good luck with your quest.