atime is heavily used by traditional mail clients like mutt, to determine which mailboxes have new mail: If atime < mtime, then there has been a write to a file since the last read.

Because updating atime on every file access carries an IO overhead, there's a mount option "relatime" that only updates atime if atime < mtime. This preserves the "new mail" feature of mutt, but doesn't require atime writes for every file read operation, which is a decent compromise.

relatime has also been the default on Linux for many years.

I've been wanting to write a program that checks atime on stuff like music and then looks for bitcoin addresses to send micropayments to (so you get something like a generalised peer to peer Spotify). I've started a couple times but kept throwing it out, all my FSs that support it are still mounted with atime. I guess I've never knowingly used it for anything else though.

We use atime at work as a proxy for "does this file really need to exist?" on our cluster's scratch disks.