What the cloud provider is always responsible for
The cloud provider is responsible for the physical infrastructure without exception. The data centers, the physical servers, the networking equipment, the power systems, the cooling, the physical security of the facilities. You will never patch a hypervisor or replace a failed hard drive in AWS. This is not configurable or optional. It is baked into every service you use.
The provider also manages the global network that connects their data centers, the hardware and software of the virtualization layer, and the managed services infrastructure. In AWS, S3's underlying storage hardware, the Lambda runtime environment, and the RDS database engine patching are all provider responsibilities.
What you are always responsible for
Your data is always your responsibility, regardless of service model. Encrypting it, classifying it, controlling who can access it, ensuring it complies with regulations. The cloud provider gives you tools to do this (encryption, access controls, compliance frameworks) but the decision to use them is yours.
Identity and access management is always your responsibility. The provider gives you IAM tools, but who you give access to, what permissions they receive, and whether you enforce MFA are all decisions you make. Credential compromise is the most common cause of cloud breaches, and it is never the provider's fault when it happens.
The responsibility for operating system configuration, network configuration, application code, and data classification shifts based on service model. In IaaS, you own all of it. In PaaS, you own the application and data. In SaaS, you own only the data and access controls. This sliding scale is the core of the shared responsibility model.
How to choose the correct answer
Provider is always responsible: physical hardware, data center facilities, hypervisor, global network infrastructure, managed service engines.
Customer is always responsible: data classification and encryption, IAM configuration and access controls, client-side encryption, regulatory compliance of data.
Depends on service model: OS patching = customer in IaaS, provider in PaaS/SaaS. Network configuration = customer in IaaS, varies in PaaS, provider in SaaS. Application code = customer in IaaS and PaaS, provider in SaaS.
Encryption: encryption at rest of customer data is a shared control. The provider offers the encryption capability (S3 SSE, Azure SSE). The customer decides whether to enable it, what key type to use, and who has access to the keys.