Oracle: year must be between -4713 and +9999, and not be 0

Single quotes (') in SQL denote string literals. So 'hiredate' isn't the hiredate column, it's just a varchar, which, of course, doesn't fit the date format you're specifying. Just drop the quotes and you should be fine:

SELECT hiredate
FROM   admin_emp
WHERE  TO_DATE(hiredate,'yyyy-mm-dd') >= -- No quotes 
       TO_DATE('2012-05-12','yyyy-mm-dd');