Where I saw it crop up was 32K folders under /tmp on a cluster system. So no it's not a limit on number of directories entirely (that's inodes), but rather how many subdirectories you can have.
http://en.wikipedia.org/wiki/Ext4#Features <-- Fixes 32K limit
Augh. I ran one of my servers hard into that wall, and now it's something I watch. At least I learned from that mistake.
Fixed by using the undocumented option isolate_network=NO in vsftpd.conf.
* lack of proper/default monitoring advocated for your tools (2), (4).
* Choosing poor (default/recommended) settings (1), (4).
* Keeping stateless server/instances when you don't need to (5), (6).
* Not tracking performance as part of monitoring (3), (4)
Albeit, I have made the same mistakes too.
edit: formatting
2) Whether your slave DB stopped replicating because of some error.
3) Whether something is screwed up in your SOLR/ElasticSearch instance so it doesn't respond to search queries, but respond to simple heartbeat pings.
4) If your Redis db stopped saving to disk because of lack of space, or not enough memory, or you forgot to set overcommit memory.
5) If you're running out of space in a specific partition you usually store random stuff like /var/log.
I've had my ass bitten by all of the above :)