There are many IT jobs that don't require programming. Here are a few:
Computer Technician - Works on computer hardware at user location or in service center. (entry level IT Job)
Service Center Coordinator - Schedules the repair of user community computers, orders spare parts, schedules staff, establishes priorities, maintains loaner laptops and non-US laptops for travel outside of US.
Help Desk Staff - answer questions and resolve problems for the user community. (entry level IT Job - Tier 1 support)
Storage Administrator - in charge of mass storage servers and devices.
Network Administrator - Works on routers, switches, hubs, cables, load balancers and all the other hardware that handles LAN and WAN network traffic. Also, may be responsible for IP phone service.
Systems Administrator or Systems Engineer- Works with servers, laptops and desktop computers to keep them free of problems and secure the data they contain. Responsible for Security group creation and memberships, server patching, anti-virus protection updates, password changes and any automated mechanisms that make these changes. These positions may be divided into server and desktop teams. Tier 2 support.
Enterprise Administrator - Handles Enterprise support and design issues. Tier 3 support.
Active Directory Administrator - Designs and administers Active Directory infrastructure, AD policies, access permissions, roles, group policies, separation of duties.
Exchange and Messaging Administrator - maintains mail systems servers, other mail related devices and the company messaging infrastructure.
Backup Administrator - Maintains backup devices and determines backup strategies so data that was deleted accidentally or intentionally can be recovered. Design and control how and when data is backed up, where the backups are stored and how long the backups are retained. They will test to be sure backups are valid and usable.
Disaster Recovery Specialist - Plans for disaster events so the company data and infrastructure can be brought back online as quickly as possible after a fire, flood, earthquake, terrorism or other disaster event. Plans for failover of services to alternate locations, if the primary location is not available.
Database Administrator - Maintains the company databases which may include customer and sales records, billing information, inventory and other data.
Computing Security Specialist - A company's biggest asset is its data and the Computing Security Specialist will work to try to keep that data protected from loss. They may be dealing with and defending against viruses, hoaxes, malware, keyloggers, phishing attacks, internal attacks and domestic and foreign intrusion. Develops monitoring and interception systems, filters and strategies and works with appropriate government agencies.
Ethical Hacker – performs intrusion and vulnerability testing of systems. Works with Computing Security to insure intrusion prevention systems are working correctly.
Corporate IT Acquisition Specialist - Works with acquired outside companies to establish migration into the corporate computing infrastructure.
Data Center Administrator - Maintains the data center facilities where the company's servers and other devices reside. They are responsible for physical security and may review badge reader and camera information to be sure that only individuals with proper access are getting close to the company's servers and other critical devices. Also, maintain backup power devices (UPS or generators).
In a small business the list of jobs above might be performed by one or two people doing all these jobs. In a large Enterprise environment this could be hundreds of people.
Best wishes!