Its a system administrator duty to be sure the ESX servers health and performance are OK.
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I believe the most important things to monitor are:
CPU check_cpu_esx (check_vmware does a great job too)
DISK check_disk (default nagios script)
VOLUMES (storage) check_vfs
VMS check_vms (how many Virtual Machines are on the server)
Memory check_vmware (by Steve Shipway, excelent script that gets info from Virtual Center)
Hardware (Fan,Temp,Arrays,Memory Dimms,Disks etc…)
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I have tested all checks with ESX 4, HP or Dell Hardware.
For the hardware checks to work you will need to install
Dell Open Manager or HP Insight Manager
These scripts can be called by using check_by_ssh nrpe, snmp.