It's very important to take a break from working at your computer every hour. Repetitious static work (working at a computer) can be very fatiguing on your upper extremities as well as your eyes. Your body needs periodic breaks to rest and recover. Taking a break does not mean you have to stop working, you could make a trip to the copier, talk to a colleague, make some phone calls, etc.
It is also very important to change positions periodically. Sitting in one position or leaning on your arms for an extended period of time can interfere with circulation. Moving around can help with circulation and prevent you from putting pressure on one location for an extended period of time.
It is often working overtime and the stress of deadline situations that force people to ignore and work through their pain and discomfort. It is very important that once you start to notice some pain or discomfort to be very careful. Pain that goes away over night is usually a sign of fatigue, pain that is continuous and does not go away over night is more serious and should be attended to immediately. Ignoring pain can lead to serious injury.
Finally be careful with what you do outside of work. Repetitive stressful activities outside of work (e.g. home improvement projects, hobbies that require repetitive motion, etc.) can sometimes lead to repetitive motion injuries as well. When working on a new task you should treat it just like preparing for a race. Whenever you engage in a new task gradually build up your strength and endurance, don't just jump right in.