Activities pane on Manage Case page
OK, I found the answer*. The file is civicrm/templates/CRM/Case/Form/ActivityTab.tpl, and the display settings for the activity tab are in line 77. Change 'desc' to 'asc'.

In the same line, you can also change the default number of lines displayed (change to one of the preset values 25, 50 or 100).

The details of this answer refer to CiviCRM 4.7.3, Joomla version. Not sure if there may be a difference with other platforms.