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.
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.)