Are you familiar at all with any scripting? VB, Perl, PowerShell? Use whatever is most comfortable...
All you need to do is
- use one of their native functions to read in environment variables. In perl, for example, reading the event's username from the command session would be: "my $eventUser = $ENV{VMWARE_ALARM_EVENT_USERNAME};"
- repeat for the other variables you are interested in, such as "my $eventDesc = $ENV{VMWARE_ALARM_EVENTDESCRIPTION};"
- use an SMTP function within the scripting tool, such as "use Net::SMTP;" in perl (if not obvious, I'm normally use perl)
- build a message body from the variables that vCenter passes to the command session, and send it. (there are tons of examples out on the 'net on how to do this)
There are lots of sample scripts up on VMTN as well. Some powershell samples can be found here: http://communities.vmware.com/community/vmtn/developer/codecentral/vsphere_powercli
If I had already coded the above, I'd be happy to share. I see value in coding this up, so if I get some time to do so, I'll post it up. If you go ahead and do it, please post for everyone to use.
It would be nice if the "Send a notification email" action in the alert settings had a template that could be modified. That would be a lot easier than breaking out to a command prompt to execute an external script... However, there are a lot of short comings in vCenter's alert function. In an external script, you could also check for time of day - maybe you don't care about particular events after 8pm at night, or maybe you want to keep track of the number of events and only execute a notification if the event happens 5 times in an hour. There's a lot more flexibility with scripting, and correspondingly more work 
Regards,