Error when rendering a template (for HTML email) on users.saveUser
The issue turned out to be the result of a variable name mistake on my part. I had typed in an incorrect variable name in the email template. I actually still don't really understand what that has to do with a database transaction, though.

EDIT:
If anyone else is running into a similar issue, I've found a way to get a more useful error message, as opposed to the "CDbTransaction is inactive" message, which doesn't help much. If you go to craft/app/services/UsersService.php, and comment out line 311 ("$transaction->rollback();"), then Yii won't give you the CDbTransaction error before Craft has a chance to tell you its more helpful error. This should give you a better idea of what you're doing wrong. Obviously, don't forget to un-comment that line after you've fixed your issue.