I've been running Ubuntu 12.04 for a while now with no problems. Overall, the only kind of instability I've had is that the system will occasionally lock up completely under prolonged full cpu usage.
My current problem, though, is that Unity constantly freezes. Often, the whole thing doesn't freeze. Usually, only part of it freezes. For example, any open windows will lock up but the launcher will remain responsive, or vice-versa.
I can find no abnormal resource use associated with these freezes, though. That and the fact that I can often restore responsiveness by clicking somewhere on the status bar at the top make me inclined to think that this is a bug in Unity, and not, say, an issue with the graphics driver.
If it's of any use, though, I do have a PCIE Radeon card for which I am using the proprietary drivers, but I was able to use this for a month before I encountered this problem.
Another thing that I've noticed is that the problem often manifests itself the most soon after a start-up. As soon as the system runs for a few minutes, the problem becomes significantly reduced. Has anyone experienced something similar, and, of so, how did you fix it?