Sure, although it's common for single people to have a pet.

I don't know about the US, but in Canada I think it's illegal for renters to discriminate against pet owners. Many still do however.

In the US, it's very common to discriminate against pet owners, either by not renting to them or by requiring extra deposit against pet-induced damage -- or even worse, just demanding extra "pet rent".

In the province of Quebec you can specify a "no pet" rule in a lease. You can even be more specific and allow for a certain number and type of animal (e.g. max 2 cats, no dogs).

There's a lot of stuff you can't discriminate on, but animal ownership isn't a fundamental right.

In Ontario, the law stipulates that a land owner may not restrict leasers from owning a pet, unless the pet runs afoul of other stuff (like if they somehow interfere with another leaser's ability to live a reasonable life). But everyone still puts the 'no-pet' clause in the contracts.