I was unfortunate enough to work at a place with a 10+ year old code base where there have been 3 to 4 software architects that have all had their own vision over the years. The code has been refactored many times already. It consisted of a buttload of singletons that were all initialized at seemingly random places. It was impossible to start or shut down the app deterministically. It was massively multithreaded (in most cases for no good reason). They had this horrible implementation of a shared cache (because many instances of this app ran across many computers that needed to share state).
It had no unit tests. Whenever you change anything it would break something entirely different. To me it was an example of everything going wrong...many times.
The best part was that it had to run for weeks because it was a critical application (for fire, police and military services). It didn't. They were instructed to reboot all the machines every day. But it wouldn't start up properly every time so they may have to do it multiple times. I did my best for the year to clean up the critical parts of it. I was contracting there but they had offered me a full time position by the end.
I finally cracked it when the original "software architect" came back because he had been fired from his old position. He was annoyed that over the years his code had been changed so he started to put back in place everything that he had done before he left. Not only that we had an angry complaint from one of the customers about a possible hostage situation that could have turned very badly because of this crappy system.
We tried to reason with the software manager by suggesting that we assign one or two people to start from scratch and take across code that can reused. It would take a bit of time to reach the same feature set as the old application but it had become so difficult to add new features to the old one that it needed to be done.