By tool I mean the access date/time stamping. Beyond that it's my peepers.
Typical usage:
"hey what happened to ...., it was fine this morning, but it just had a melt down?"
"config file was last modified xx/xx/xx at xx o'clock. Who was working then?"
Or, as we unfortunately have seen in the past far too often:
support ticket - Hello, I've been getting a lot of email bounces for emails I haven't sent, can you tell me what's going on? It's been happening since Saturday.
A quick ls sorted by date reveals that the client's handy dandy php ad rotator or perl mailing system has been altered on Saturday. Or that there is a new file named a.pl dated that Saturday which upon examination turns out to be a perl based shell that was uploaded through an old phpmyadmin exploit.
These are things that would strike me as slower to do with atime off.
Again, your own site's rick assessment will determine whether this is an issue or not. If you are the only one that ever touches your files it might not be much of an issue at all. As someone that spends a lot of time finding, cleaning up, then explaining various messes I find it pretty indispensable.