Mostly problems with the graphical stuff. More than once I've had to log in via a text console and mv ~/.kde somewhere else to start X, or move some ~/.Xfoobar file. Once some ~/.Xfoobar file filled up the entire /home/ partition due to some X error. I've also had problems with some network card driver on a new install, I can go through my posts on unix.SE if you want more detail.
I simply remember that Ubuntu should only be updated when I've got a spare day to fix any potential issues, whereas so far CentOS can be updated before each shutdown.
All this is from the perspective of a desktop user. I use both on various web servers and I've found both to be reliable. I'll use CentOS where I need absolute stability but on my cloud instances I'll happily use Ubuntu and get the latest PHP, etc.
