Today this error happened to me, too, and I became aware of why it can happen (among possible other reasons).
APC correctly identifies every class by a fully qualified name, which includes the classes namespace. Unfortunately you can end up referring to the same class with various names.
For example:
I had a wrong "use" statement in my code, importing a non-namespaced class as if it had been inside a namespace.
The class, say "MyClass" was in namespace "\", meaning that its correct and fully qualified name was "\MyClass".
At some point the class was referred to by its unqualified name "MyClass", and got autoloaded. In another file I (wrongly) referred to the class with a namespace prefix in a use statement, say "use \SomeNamespace\MyClass;". Consequently the class was (again) passed to my global __autoload() method, but with a different name. To make it worse, the autoload method was smart enough to find the class anyway.
Instantly, my script stopped working and all that happened was APC writing "[apc-error] Cannot redeclare class ..." into the Apache Web Server error.log. My pages were no longer available.
This is not an APC bug whatsoever, but simply correct behaviour.
In my case it helped to temporarily disable APC (so that my script would be run regardless of the conflict), and hook an echo statement into my __autoload function producing a list of the parameters passed. The class loaded with a wrong name would show up quickly, and I could fix it and reenable APC.
Hope this helps someone.