Well, since the OP stated "I am looking for a backup utility that can look at a directory or file and tell if it has been changed..." I am assuming he is not looking for a system backup utility as Drive Image/Ghost would provide. Instead, it sounds as if he has specific data folders that need to be backup up on a regular basis.
And, if he is like me, he shuts his computer down at night, so doing a backup at night is not an option.
As stated, most backup software should have that capability. Which one you use will depend upon the level of configurability. Free or cheap products may only have limited options for selecting the backup locations, creating rule sets (e.g. don't backup .mp3 files), or for scheduling the backup. They will also depend upon your level of expertise.
Without additional information, I would suggest the "Replicator" application which is part of the free KarenWare products.
http://www.karenware.com/powertools...
Michael J