We use it in a traditional way. We replaced an older system based on Nagios, and we had problems with false positives. We install the Zabbix agent on the client hosts and set up automatic installs. The agent is added to these other client hosts, and we have the infrastructure in place to support static servers.
Then we write the rules to tell Zabbix how we want it to report, and then let it run. If we've got a critical error, someone will be notified. Otherwise, we get an email message that a server is having a problem.
Sometimes, the problems resolve themselves, and sometimes, they don't, and we have to take action. But it's mostly hands-off for the most part. It's doing very well for that.
It has improved our overall server performance monitoring. We know right away when there are problems. It has built-in statistics, so we can identify if there's spiking. We can see what's happening every day around the same time and check the configuration to see if there's something that's malfunctioning and needs to be fixed. As we get better at diagnosis, we can go back and look at the history of the systems to pinpoint problems.