Should I put OLAP and realtime web DBs on the same server? I have several different workloads I'd like to consolidate into the same Sql 2012/2014 instance.


Cognos/OLAP is burst oriented and users are accustomed to a response delay 
Web databases that require immediate response (user authentication)


Is there any way to leverage SQL to partition these workloads?
You can install both on the same instance, If the performance is an issue you can use the resource govenor to make sure that the web database gets the lion's share of the resouces. 

Security wise I would reccomend to separate the two by using different instances but if you are careful in setting up security this should be no issue.