JIRA: Is it possible to set issue assignee based on "Issue Type" automatically?

Create separate workflows for each issueType.
Create a workflow scheme for your project mapping those workflows to the specific issueTypes.
Then (in the workflows) using the stock post function "Update Issue Field", set your Assignee field to the desired user for each individual issue type in the "Create" transition.

3 things to note: 1.) To get to the "Create" transition, click on the "Open" step and "Create" should be one of the Incoming Transitions. 2.) When adding the post function, be sure to place it after the "creates issue originally" function or you will get some nasty errors. 3.) Be sure to delete the post function "Assign the issue to the reporter" otherwise your issue will get re-routed to the reporter.