I'm moving this over to our Server Administration section where hopefully our fellow Server Admins can give you a good answer.
There is no way to set up SNMP traps on Tableau Server that I know of. There are no OIDs that you can monitor.
The best thing i can think of would be setting up a script that monitors the xml status output and provides alerts however you program it. here's the xml process: Monitoring the Status of Tableau Server | Tableau Software
You could try monitoring the Tableau process JVM's using JMX. you can configure this in tableau here: http://onlinehelp.tableau.com/current/server/en-us/help.htm#ports_jmx.htm
Hope this helps
As far as I know there's no way to do this and I agree it would be useful, especially in large enterprises.
At my org we run our enterprise monitoring tool (Microsoft SCOM) on the Tableau Servers and configure our own alerts for process, disk, memory, CPU etc. SCOM then sends alerts to a Netcool Console manned by an offshore L1 team who then call out accordingly. We also have some extra monitoring using scripts and windows scheduler to provide an extra level of checking in case the enterprise process fails. It's good to be paranoid when it comes to monitoring.
There's a lot to consider when setting up monitoring of your Tableau Server. Check these posts for more details.
We have Enterprise monitoring in place for Tableau by doing the following 3 checks:
1. the Windows team has checks to verify that the servers are operational and they get alerted if something goes awry.
2. Every 5 minutes our in-house monitoring does an http status check on the prod url. The expected response is a 302
3. Every 5 minutes, the monitoring looks at the system admin status XML page and checks for OK.