(Disclaimer: we don't actually have a formal DBA position; most of the data systems we have were built by contractors and have been maintained by people with little to no DBA experience.  I've been with the company for less than a year, in which time my boss has expressed a fervent desire to get out of reactionary mode and into a more proactive state.  Unfortunately it sometimes takes a serious disaster to convince managers of the importance of preparation.)

We found out the hard way last year, that most of the legacy systems the company has been using for 10+ years didn't even have backups.  So, some of those machines will never be rebuilt.  But even for the systems that had backups, we had little to no idea of how to go about rebuilding systems that we didn't have good documentation on.  So our emergency mode lasted for almost 2 months, and 3 months later, we're finally working on outlining and implementing backup and DR practices that will keep us from such a nightmare happening again.  Luckily our system is just the place we aggregate data from multiple different sources, so business didn't quite grind to a halt during our recovery.  We just had a lot of very frustrated analysts.