mutt, an email client, uses file access times to monitor for new mail arriving on an mbox-formatted mailbox. Apparently, this problem is not serious, and is easy to work around.
Other than that, it is difficult to find examples of things that break on noatime. I run a number of Linux servers with noatime on all filesystems, and I can't recall ever having seen any problems attributable to noatime.
If you are concerned about using noatime in general, you could devote a separate filesystem for your mongoDB stuff, and mount only that filesystem with noatime.
EDIT
I found an interesting blog at kerneltrap.org that quotes some discussions between Linux developers (Linus Torvalds, Ingo Molnar, Alan Cox, and others) on the topic of atime. In Ingo's second email, he says this:
... i've got no real complaint about
ext3 - with the obligatory qualification that "noatime,nodiratime" in
/etc/fstab is a must. This speeds up things very visibly - especially
when lots of files are accessed. It's kind of weird that every Linux
desktop and server is hurt by a noticeable IO performance slowdown due
to the constant atime updates, while there's just two real users of it:
tmpwatch [which can be configured to use ctime so it's not a big issue]
and some backup tools. (Ok, and mail-notify too i guess.) Out of tens of
thousands of applications. So for most file workloads we give Windows a
20%-30% performance edge, for almost nothing.