*Disclosure: I am a Genetec employee*
Genetec Security Center offers a very easy way to accomplish exactly what you describe: using the "System Status" task, you can actually see, in real time (and dynamically, so the status of a camera can change while the report is opened) if a camera is online/offline and recording/not recording. The list of cameras can also be sorted, i.e. show all non-recording cameras first.
This report could also saved and sent to anyone in the organization in the form of a CSV, XLS of PDF file. The report can also be used to see the live status of servers, doors, access control units, elevators, intrusion area and much more.
You can also create live actions (pop-up message, email, alarm, etc) when a camera event happens (motion, input/output, no signal, etc).
Let me know if you'd like more information, I'll be glad to help.