Scalability: A well-designed system must, first and foremost, be scalable. As traffic increases, the system must still operate efficiently.
Reliability: In the end, scaling a system doesn't matter if it's not designed correctly. As an example of reliable system design, the system will continue to run even if a user makes a mistake, as well as prevent unauthorized abuse or exploits.
Accessibility: A highly accessible system is necessary for a reliable system to function. A reliable system will be able to continue to function over the years. Or put another way, uptime/total time.
Efficiency: Unless a system is efficient, it's hard to call it well designed. An efficient system is one that works quickly.
Maintainability: Finally, maintenance. It must be easy for other engineers to modify and maintain a system over time: the operation must be straightforward.