I may re-assign issues in any of 3 ways:

1. Use the Assign To Operation
2. Edit the Assign To while editing the issue.
3. Perform a bulk edit on a number of issues and change the Assign To

There are many reasons why I might use the latter 2 - because as I am scheduling issues for versions and due dates I am also re-assigning the developer. However, it appears that no notification is being sent out to the new assignee if I use one of those options unless I also include the "Current Assignee" to be notified on an "Issue Updated" event.
I prefer not to inundate users with emails about every update on an issue that is assigned to them, which is why my notification scheme did not include that. I believe that if part of the issue update/edit was also to re-assign it, JIRA should be smart enough to realize that this is also an "Issue Assigned" event.

I realize you may consider this a duplicate of JRA-6344, but in that issue it claimed that bulk edit assignee did send out a notification. And also, I do not believe this is an improvement request. I think it is a bug.