Are there landlords who do not require the renter to sign a written contract or other legal form to rent an apartment?

Get SOMETHING in WRITING!!!! A handwritten note signed by them is a CONTRACT! good luck :) There are some, they're generally called "fools". The contract can be written to protect the interests of the renter and the landlord. The contract just clarifies responsibilities. Don't consider it to always be a bad thing. Writing down the terms of the rental and having everyone sign it just makes things clear later.