vCenter comes with a few default alarms such as ESX host connection state and usage alarms.
These are useful but only are visible if you are logged into vCenter with VI Client.
However it can be configured so that you get email alerts when these alerts trigger between a certain status.
At the "Hosts & Clusters" level click on the "Alarms" tab.
Change the view button to "Definitions".
Choose the Alarm you want to setup and email notification for right click "Edit Settings".
In the Alarm Settings dialog go to the "Actions" tab.
Add an action to "Send a notification email" and set an email address as the value.
Tick the status changes you want to be emailed about. Click Ok.
Now when there is a status change in the defined trigger you will receive an email alert.
Note: Be sure you have set an SMTP server in the virtualcenter configuration under the administration menu.