A small number of users have reported not being able to login to the front end in Joomla 2.5.13.
This seems to only occur when the users have a corrupt asset table.
This is usually due to a faulty migration from Joomla 1.5.
To check this, look at your asset table in your database. If there is more than one parent_id with a value of 0 this indicates a corrupt table.
SELECT count(*) FROM `#__assets` WHERE parent_id = 0
Apply your own prefix instead of #_.
There should only be 1, only the root asset is allowed to have parent_id=0.
To fix you can manually or with an sql query change the parent ids. If the broken assets are categories the parent should be set to the id number for that component (for example usually the id for com_content is 8). (They can also be set to have a parent of another category in the same component.)
For something besides a category, set the parent either to a category id or to the id for the extension if the extension does not use categories.