You just knew someone was going to come in here pointing out that they knew of a landlord that drafted their lease on the back of a used Kleenex. Well. I stand corrected, then.
What? I didn't say that, at all. I'm just saying there are a ton of cases where landlords don't require leases to be signed. Credit checks and references are less common than leases. I live in Chicago and in a big city like this one, there are many, many different renting situations (not just "Kleenex" ones) and not all of them contractually come in conflict with a renter having someone pay to live in part of an apartment.
I live in Chicago and rented in Chicago for many years and I never saw a lease that hadn't been drafted by a lawyer. Most leases are boilerplate --- let alone rentals without leases. If you're renting an apartment without a lease, something shady is going on.
But look, in the meantime, can we just implicitly narrow the conversation down to the normal case of "renters with actual leases"? This is a stupid tangent. Obviously there are landlords who don't give a shit if people in their buildings convert apartments to hotels, just as there are buildings where the other tenants don't care either.
A rental without a lease? That sounds like a friend renting our a spare bedroom to another friend. I would propose that without a lease, it ceases to be a rental, because neither side has any obligation to the other.
I, like the others in this thread, can only speak to Chicago laws. Here, a verbal lease is a perfectly valid lease, subject to the laws of the city and state (we usually call it "month-to-month"). I wouldn't say it's exactly common, but it's not exactly uncommon either. My last apartment was rented month-to-month for 4+ years (and was a nice apartment with a nice landlord).
In the cases I'm most familiar with, the apartment starts with a lease, and rather than renew the lease specifically, just shifts to a verbal lease, provided the landlord and tenant trust each other. (Were I renting an apartment to someone else, there isn't a chance in hell I would do it without a lease, though.)
I really have to object to the idea that verbal leases are common in Chicago. I think if you set out to find an apartment, an attached house, a carriage house, or a freestanding house today, you'd have a very hard time finding one that didn't have a written lease attached to it.
But obviously this is a tangent. To whatever extent verbal leases are common or not, it's impossible to argue that formal written leases are uncommon. They are the norm.