The core list is fairly universal: a valid passport, your visa or residence permit, and proof of a local address. Address proof is the one that trips most newcomers up, since utility bills take months to arrive in your name. Banks in many countries accept alternatives like a rental contract, a landlord letter, an employer confirmation, or university accommodation documents, so always ask what substitutes they take.
Beyond that, expect requests for a local tax number or your home-country tax ID, an employment contract or student enrollment letter to show income source, and sometimes a local phone number for verification codes. A few countries also want an initial deposit to activate the account.
My practical suggestion is to carry a document folder for your first month abroad with passport copies, visa, contracts, and passport photos, because the same bundle that opens a bank account also gets you a phone plan and a rental.